AN ECONOMETRIC CHARACTERIZATION OF BUSINESS CYCLE DYNAMICS WITH FACTOR STRUCTURE AND REGIME SWITCHING * Marcelle Chauvet 1

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "AN ECONOMETRIC CHARACTERIZATION OF BUSINESS CYCLE DYNAMICS WITH FACTOR STRUCTURE AND REGIME SWITCHING * Marcelle Chauvet 1"

Transcription

1 AN ECONOMETRIC CHARACTERIZATION OF BUSINESS CYCLE DYNAMICS WITH FACTOR STRUCTURE AND REGIME SWITCHING * Marcelle Chauve Deparmen of Economics Universiy of California, Riverside 5 Universiy Avenue Riverside, CA A dynamic facor model wih regime swiching is proposed as an empirical characerizaion of business cycles. The approach inegraes he idea of comovemens among macroeconomic variables and asymmeries of business cycle expansions and conracions. The firs is capured wih an unobservable dynamic facor and he second by allowing he facor o swich regimes. The model is esimaed by maximizing is likelihood funcion and he empirical resuls indicae ha he combinaion of hese wo feaures leads o a successful represenaion of he daa relaive o exan lieraure. This holds for wihin and ou-of-sample and for boh revised and real ime daa. Running Head: Business Cycle Dynamics KEY WORDS: Asymmeries, Business cycles, Comovemens, Dynamic facor model, Kalman filer, Markov swiching. JEL Classificaion: C32, C5, E32 * Manuscrip submied in January 996. This paper was wrien wih financial suppor from CNPq - Brazilian Council for Scienific and Technological Research. This maerial is based on my docoral disseraion from he Universiy of Pennsylvania. I am graeful o my advisor Frank Diebold for his invaluable advice during all sages of his research. I also hank James Hamilon for helpful suggesions. The auhor bears full responsibiliy for any errors.

2 . INTRODUCTION A grea deal of aenion has focused on measuring business cycles and idenifying heir urning poins. The possibiliy of a se of indicaors providing early signals of change in aggregae economic aciviy is imporan o any business or governmen affeced by expansions and conracions. Based on he early work of Burns and Michell (946), he U.S. Deparmen of Commerce consrucs economic indicaors ha are widely used o predic business cycle urning poins. Burns and Michell provide a careful saisical descripion of he cyclical aspecs of various ime series, and classify macroeconomic variables as lagging, leading or coinciden wih economic aciviy. However, he analysis does no provide a formal mahemaical reamen of business cycle measuremen. In paricular, an explici probabiliy model generaing he aggregae ime series is lacking. As a resul, he Deparmen of Commerce indicaors do no conain all he informaion necessary o characerize business cycle dynamics a he ime he evens occur and are consanly revised ex-pos. The NBER daing of business cycle urning poins is also based on a poseriori inferences of coinciden variables. Since revisions of he indicaors can be subsanial, real ime assessmen of economic condiions may be severely compromised. This paper proposes a heoreical framework in which a formal underlying probabiliy model is used o represen business cycles and o generae coinciden indicaors and inferred probabiliies of expansions and recessions. The resuls are reproducible, and he mehod enables analysis of business cycles in real ime. For example, he imminence of a recession saring in a cerain monh can be deeced by he inferred probabiliies or by he implied coinciden indicaor a he same ime he macroeconomic variables are signaling he recession. In he proposed model, business cycles are empirically characerized by a dynamic facor model wih regime swiching. The dynamic facor is an unobservable variable ha

3 summarizes he common cyclical movemens of some coinciden macroeconomic variables. This facor is subjec o discree shifs in order o capure he asymmeric naure of business cycle phases - expansions are gradual and display a high mean duraion while recessions are shorer and seeper. Hence, he approach used in his paper models he idea of business cycles as he simulaneous movemen of economic aciviy in various secors by using an unobserved dynamic facor. In addiion, he asymmeric naure of expansions and conracions is capured by assuming ha he underlying facor swiches regimes according o a Markov process. Boh of hese ideas were fundamenal elemens of Burns and Michell s (946) research. The wo elemens, however, have been sudied separaely. On he one hand, Sock and Wason (989, 99, 993) develop a model where business cycles are measured by comovemens in various componens of economic aciviy in order o obain an alernaive index o he Deparmen of Commerce indicaors. Recessions (expansions) are generaed by negaive (posiive) symmeric shocks o a linear and dynamically sable ime series sysem. Unforunaely, Sock and Wason s model fails o accoun for he 99 recession using a recession index exraced from heir nonswiching dynamic facor represenaion. The lineariy imposed by heir model implies a buil-in symmery which forces expansions and conracions o have he same magniude, duraion, and ampliude. In addiion, Sock and Wason s model does no ake ino accoun changes over ime in he sochasic srucure of he economy, such as shifs in policy, while an analysis of he long erm rend of aggregae macroeconomic ime series such as employmen, sales, and oupu indicaes several srucural changes over his cenury. On he oher hand, Hamilon (989) considers nonlineariies in business cycles by assuming ha he growh rae of quarerly GNP follows a nonlinear saionary process and incorporaes occasional discree variaions in he dynamic feaures of his ime series wih a Markov 2

4 swiching model. He finds evidence of asymmeries in cyclical expansions and conracions and ascerains he differences in he dynamics of business cycle phases. However, Hamilon s model, since i is univariae, can no capure he noion of economic flucuaions corresponding o comovemens of many aggregae and secoral variables. In addiion, exensions of Hamilon s analysis o monhly growh raes fail o accoun for several of he hisorical recessions as deermined by he NBER. I is possible ha all underlying business cycle informaion can no be exraced from only one coinciden variable. Also, individual coinciden variables display movemens ha do no correspond o business cycle dynamics bu insead o noise inheren in monhly daa. Diebold and Rudebusch (996) sugges inegraing he wo ideas by fiing a univariae Markov model o he Deparmen of Commerce coinciden index and o is componens. They show evidence of he suiabiliy of a swiching dynamic facor, alhough hey do no fully esimae i. The exising lieraure has no found a generally acceped framework ha provides a unified explanaion of business cycle asymmeries and he comovemens of economic aggregaes. In his paper, we consruc an inegraed represenaion of wha Sock and Wason and Hamilon pursued in separae frameworks, as suggesed in Diebold and Rudebusch (996). The idea is ha he inegraed approach migh capure in large par wha Burns and Michell and he NBER have in mind in heir descripion of business cycle comovemens and asymmeries. The novel aspec of his paper wih respec o he exising lieraure is ha we fully esimae a dynamic facor model wih regime swiches by maximizing is likelihood funcion. Mehods for esimaing his model were no available unil recenly. To esimae he model i is necessary o make inferences abou boh he unobserved nonlinear facor and he laen 3

5 Markov sae. Hamilon s (989) paper popularized he use of Markov regime swiches, bu he nonlineariy inroduced by his precluded he esimaion of mulivariae unobservable dynamic models. In paricular, Hamilon s nonlinear esimaion algorihm can no handle models wih a regime swiching dynamic facor. The dynamic facor model proposed by Sock and Wason s (989, 99, 993) is governed by a linear sochasic process, which implies ha he esimaion can be implemened by applying he Kalman filer. The esimaion procedure underaken in his paper consiss of a combinaion of Hamilon s algorihm and a nonlinear discree version of he Kalman filer, as proposed by Kim (994). The goals in building a dynamic facor model wih regime swiching are o obain opimal inferences of business cycle urning poins, and o consruc alernaive coinciden indicaors o he Deparmen of Commerce coinciden index. The empirical resuls indicae ha he combinaion of a dynamic facor model wih Markov swiches leads o a successful represenaion of he sample daa, relaive o he exising lieraure, along several dimensions. This holds boh wihin and ou-of-sample, and for boh revised and real ime daa ses. In paricular, he resuls corroborae previous evidence abou asymmeries of business cycle phases. The inferred probabiliies are srongly correlaed wih he NBER business cycle daes and all recessions are well characerized for boh quarerly and monhly daa. In addiion, he exraced coinciden index is srikingly similar o he Deparmen of Commerce coinciden indicaor. However, he advanages of he presen framework in comparison o radiional approaches are ha i allows a more rigorous and imely mehod for real ime assessmen of he economy, and resuls can be consisenly reproduced. In conras, he Deparmen of Commerce and he NBER mehodologies require ex-pos revision in order o obain resuls ha we are able o aain in real ime. 4

6 The paper is organized as follows: he second and hird secions presen he model and discuss he esimaion procedure employed in our sudy of he swiching dynamic facor framework. In he fourh secion, he empirical resuls are presened and inerpreed for boh quarerly and monhly daa. In he fifh secion, he model is esed for ou-of-sample performance and he sixh secion concludes and suggess direcions for fuure research. 2. THE MODEL A vecor of macroeconomic variables displaying comovemens wih aggregae economic condiions is modeled as composed of wo sochasic auoregressive processes - a single unobserved componen, which corresponds o he common facor among he observable variables, and an idiosyncraic componen. 2 A sochasic rend is no included in he dynamic facor based on evidence ha each of he series sudied migh be inegraed bu no coinegraed. 3 Therefore, he empirical analysis is underaken using he log of he firs difference of he observable variables. The model is: () Y i = λ i (L) F + v i i =,...,n nx nx x nx (2) F = α S + α 2 + φ(l) F - + η s S =, x x x x x x (3) v i = D i (L) v i- + ε i i =,...,n nx nxn nx nx The assumpions of he model are: 2 The coinciden variables considered are sales, personal income, employmen and producion. 3 We performed a Dickey-Fuller es (979) for he presence of uni roos in each of he coinciden variables and i was no able o rejec he null hypohesis of inegraion agains he alernaive of saionariy a he % level. We also esed wheher he four coinciden variables are no coinegraed agains he alernaive of coinegraion using Sock and Wason s (988) es, and i failed o rejec he null. 5

7 η s ~ N(, σ 2 ηs ) ε i ~ i.i.d. N(,Σ) H s ~ NI Σ 2 σ ηs D i (L) = diag(d (L),..., d n (L)) M p ij = Prob[S =j S - =i], p = i for M saes which implies ha F and v i, for i =,..., n are muually uncorrelaed a all leads and lags. The vecor Y i is he log of he endogenous observable variables, he parameers λ i are he facor loadings, which measure he sensiiviy of he i h series o he business cycle, and F is he common facor. In addiion, he variables v i are he idiosyncraic erms, he ε i are he measuremen errors, and η is he ransiion or common shock. The funcions λ(l), φ(l) and D(L) are finie lag polynomials of orders l, f and b, respecively, where L is he lag operaor and =-L. A nonlinear srucure is inroduced in he unobserved index in he form of a firs order wosae Markov swiching process. The mean growh rae of he dynamic facor is direcly calculaed from he nonlinear filer and i is subjec o sporadic discree regime shifs. Tha is, he economy can be eiher in a sluggish growh sae, S =2, or in an acceleraed expansion period, S =, wih he alernaion beween regimes ruled by he oucome of a Markov process. The facor mean or he facor variance swich beween saes, governed by he ransiion probabiliies of he Markov process, p ij. For example, Prob[S = S - =] = p is he probabiliy of an expansion given ha he economy is expanding, and Prob[S =2 S - = 2] = p 22 is he j= ij 6

8 probabiliy of recession given ha he economy is in a recession. 4 In he proposed model, cycles are generaed from common shocks o he dynamic facor, η s, and all idiosyncraic movemens arise from ε i. The only source of comovemens among he observable variables comes from he dynamic facor, which can be inerpreed as he business cycle. 5 The idenificaion of he model is discussed in an appendix ha is available from he auhor on reques (see also Chauve 995). A paricular sae space represenaion for he swiching dynamic facor ()-(3), wih an AR(2) process for he facor and an AR() for he idiosyncraic erm, is: 4 We also consider anoher specificaion for he facor mean suggesed by Hamilon (994), in which he shifs depend on he dynamics of he auoregressive process, ha is, φ(l) ( F - µs) = ηs, for S =,. This specificaion requires ha he order of he Markov swiching process be a leas as long as he degree of he polynomial φ(l). Boh models were esimaed and compared using he same number of lags for he Markov process. However, anicipaing he empirical resuls, his equaion was slighly dominaed by model (2), boh by specificaion ess and in erms of performance in predicing business cycle urning poins. Oher variaions on he basic models were also inroduced, such as allowing he facor variance and mean o swich regimes, or holding he mean consan wih a swiching variance for he facor. 5 The number of facors underlying he variables was verified by he usual procedure underaken in exploraory facor analysis. Tha is, we check he eigenvalues of he correlaion marix conaining he par of he oal variance ha is accouned for by he common facors. The magniude of he eigenvalues for each facor, which conveys informaion abou how much of he correlaions among he observable variables a paricular facor explains, indicaed srong evidence for he single facor srucure. 7

9 8 Measuremen Equaions: Y Z ξ (4) Y Y Y Y F F v v v v F = λ λ λ λ * Transiion Equaions: ξ α ξs T ξ - u (5) F F v v v v F S d d d d F F v v v v F s = α α φ φ η ε ε ε ε + * or (4 ) Y = Z ξ (5 ) ξ = α ξs + T ξ - + u Noice ha he erm F - is included in he sae vecor o allow esimaion of he dynamic facor in levels from he ideniy F - = F - - F ESTIMATION PROCEDURE We simulaneously esimae he dynamic facor model wih regime swiching by maximizing is likelihood funcion. In order o esimae he model i is necessary o make inferences abou boh he unobserved nonlinear facor and he laen Markov sae. The nonlineariy imposed by he regime shifs precluded he esimaion of a mulivariae dynamic

10 model unil he esimaion mehods by Alber and Chib (993), Shephard (994) and Kim (994) were developed. 6 We use mehod developed by Kim (994) o esimae our model. In ha paper, Kim exended Hamilon s Markov-swiching model o a general dynamic linear sae-space framework where boh he measuremen and he ransiion equaions are allowed o swich regimes. The parameers of he model are dependen upon a sae variable S, which follows a sochasic process. A nonlinear discree version of he Kalman filer is combined wih Hamilon s nonlinear filer in one algorihm. This permis esimaion of he unobserved sae vecor as well as he probabiliies associaed wih he laen Markov sae. An ineresing aspec of Kim s filer for he presen analysis is ha his algorihm combines he esimaion mehods underaken by Sock-Wason and Hamilon, while he proposed model inegraes he frameworks underlying heir models. The objecive of Kim s nonlinear filer is o form forecass of he unobserved sae vecor and he associaed mean squared error marices. The forecass are based on informaion available up o ime -, I - [ Y -, Y -2,..., Y ], on he Markov sae S aking on he value j, and on S - aking on he value i: 7 6 Alber and Chib (993) and Shephard (994) proposed, independenly, a modified version of he Gaussian filering and smoohing procedures. They employ simulaion and Gibbs sampling o obain he exac likelihood funcion of a nonlinear ime series. Basically, a Gaussian sae-space is used o analyze non-gaussian frameworks hrough simulaion echniques, and he approach may be used o find maximum likelihood esimaes of he Markov swiching model. However, his mehod is sill very cosly in erms of compuaion ime. 7 In he empirical exercise, we chose o esimae he model including an addiional sae variable, s-2, o obain (h,i, more efficien esimaes. In his case, equaions (6) and (7) become, respecively: ξ j) - =E(ξ I-, S=j, S-=i, S-2=h) (h,i, and P j) - = E[(ξ - ξ -)(ξ - ξ -)' I-, S=j, S-=i, S-2=h)]. 9

11 (i, j) (6) ξ - (i, j) (7) P - = E( ξ I -, S = j, S - = i) = E[( ξ - ξ - )( ξ - ξ - )' I -, S = j, S - = i)]. For z lagged saes condiioning he forecass and M regimes, he algorihm calculaes M z forecass for each dae, corresponding o every possible value of S -z. The filer uses as inpus he join probabiliy of he Markov-swiching saes a ime -2 and - condiional on informaion up o -, {Prob(S -2 =h, S - =i I - )}; an inference abou he sae vecor using i, j informaion up o -, given S -2 =h and S - =i, ha is, {ξ - - }; and he mean squared error i, j marices, { P - - }. The oupus are heir one-sep updaed values. For he probabiliies we use as an iniial condiion he probabiliies associaed wih he ergodic disribuion of he Markov chain. For he sae vecor, is uncondiional mean and uncondiional covariance marix are used as iniial values. 8 The nonlinear filer racks he course of he sae vecor, which is calculaed using only observaions on Y, and compues recursively one-sep-ahead predicions and updaing equaions of he sae vecor and he mean squared error marices. The par of he filer ha corresponds o a nonlinear discree version of he Kalman filer, applied o he paricular sae-space (4)-(5) is: ( 8) ( 9) ( ) ( ) (i, j) ξ = α + Tξ - (i, j) - j i - - i - - P = TP T' + H ξ (i, j) (i, j) (i, j) = ξ + K N - P = (I - K Z)P (i, j) (i, j) (i, j) - j (i, j) - (predicion equaions) (updaing equaions) 8 i The uncondiional mean and variance-covariance marix of he sae vecor are, respecively, ξ =E(ξ) and i P i =T P T +σ 2 ηs. The uncondiional mean of he probabiliies are {Prob(S-2=h, S-=i I-}=Prob(S=i)=πi, i=,2, where πi is he ergodic probabiliy.

12 (i, Here, K j) (i, j) (i, j) (i, = P Z'[Q ] is he Kalman Gain, N j) (i, j) - = Y - Z ξ - is he condiional forecas (i,j) (i, j) error of Y, and Q = ZP Z' is is condiional variance. The nonlinear filer allows recursive calculaion of he prediced equaions, given he parameers in T, Z and H and iniial condiions forξ j and P j. In he second par of Kim s filer, he probabiliy erms are compued using Hamilon s nonlinear filer. This provides he condiional probabiliy of he laen Markov sae a ime. The condiional likelihood of he observable variable is evaluaed as a by-produc of he algorihm a each, which allows esimaion of he unknown model parameers. The log likelihood funcion is: T M M -n/2 (i, j) / 2 (i, j)' (i, j) (i, j) (2) LogL= log f( Y T, Y T-,... I ))= log exp( )} = j= {(2π Q N i= Q N 2 The filer evaluaes his likelihood funcion, which can be maximized wih respec o he model parameers using a nonlinear opimizaion algorihm. The parameers esimaed and he sample daa are hen used in a las applicaion of he filer o draw inferences abou he dynamic facor and probabiliies based on informaion available a ime. 9 For each dae he nonlinear filer compues M z forecass, which implies ha a each ieraion he number of cases is muliplied by M, where M is he number of regimes and z is he number of saes condiioning he forecass. Thus, if he filer does no reduce he number of erms a each ime, i becomes compuaionally unfeasible even in he simples wo-sae case. Kim proposed an approximaion inroduced hroughξ j and P j for >, based on he work of Harrison and Sevens (976). The approximaion consiss of a weighed average of he 9 We also obain full sample inferences abou he sae vecor and unobserved regimes using Kim s (994) smoohing algorihm.

13 updaing procedures by he probabiliies of he Markov sae, in which he mixure of M z Gaussian densiies is collapsed, afer each observaion, ino a mixure of M z- densiies. Tha is: ξ M (i, j) Prob[ S ξ j = i,s = j I ] i= = Prob[ S = j I ] P M (i,j) j (i, j) j (i,j) Prob[ S = i,s = j I ]{ P + ( ξ ξ )( ξ ξ )'}. Prob[ S = j I ] j i= =, 4. EMPIRICAL RESULTS Daa The empirical analysis focuses on boh quarerly and monhly daa. For he monhly sudy, he daa sample is from o 993.3, and for he quarerly, from o The goals are o obain opimal inferences of business cycle urning poins and o consruc alernaive coinciden indicaors o he Deparmen of Commerce coinciden index. Thus, we focus on he same four secoral variables uilized by he NBER and he Deparmen of Commerce, which were seleced based on he work of Burns and Michell (946). The series This filer is an opimal esimaor in he sense ha no oher esimaor based on a linear funcion of he informaion se yields a smaller mean squared error. Smih and Makov (98) examine he naure of his approximaion hrough simulaions o verify is performance in erms of jump esimaion and deecion as well as is fi o he opimal soluion. Using an exensive range of iniial condiions for he inpus and saring parameer values, Smih and Makov conclude ha he approximaion performs well in erms of minimizing he sum of he squared errors compared wih oher nonlinear approximaion mehods. Also i is he mehod ha racks mos closely he rue observaions and i is he bes in esimaing he jumps. The sample range was chosen o be close o he one used by Hamilon, in order o faciliae comparisons. Esimaions were also performed for daa prior o 952 and he resuls are similar o he ones obained here. One difference is ha he probabiliy of saying in a recession is smaller, which may be explained by he magniude of sudden changes in he growh of he variables sudied during he 4s. 2

14 used include manufacuring and rade sales in 982 dollars (MTS), oal personal income less ransfer paymens in 987 dollars (PILTP), employees on nonagriculural payrolls (ENAP), and indusrial producion (IP). As alernaives, we also examine gross domesic produc (GDP), hours of employees on nonagriculural payrolls (HENAP), oal civilian employmen (TCE), and non-agriculural civilian employmen (NACE). 2 In boh quarerly and monhly sudies, he daa are ransformed by compuing one hundred imes he firs difference of he logarihm of each series. 3 The swiching facor coinciden index (SFC) esimaed in his paper is compared o he Composie Coinciden Index of he Deparmen of Commerce (CCI 982=) and he coinciden index proposed by Sock and Wason (SW). The series SW uses he same variables as CCI wih he excepion of employees on non-agriculural payrolls (ENAP), which is subsiued wih hours of employees on non-agriculural payrolls (HENAP). Model Selecion and Specificaion Tess Several differen specificaions of he various models were esimaed, including AR(), AR(2) and AR(3) processes for he facor in he ransiion and measuremen equaions, AR() and AR(2) for he idiosyncraic erms, and combinaions of hese using differen coinciden variables. More highly parameerized models were also esimaed, bu he coefficiens of 2 The daa, kindly supplied by Frank Diebold and Glenn Rudebusch, were obained from he Federal Reserve Board s daabank, released in June We also esimaed he model using linear derended series as well as by applying he H-P filer derending echnique. Under he linear derending mehod, if a srucural break in he 7s is no aken ino accoun, he sample daa idenify he swiching as permanen changes raher han cycling back and forh. On he oher side, he H-P filer is designed o remove aspecs of he daa, such as low frequency cycles. Thus, since our goal is o uncover dynamics underlying he daa wihou imposing any a priori informaion on i, hese derending mehods urn ou o be inappropriae for his paper. 3

15 higher dynamic orders were no significan a he 5% saisical level. 4 Akaike Informaion Crierion, Schwarz Crierion and he likelihood raio es were used o choose among alernaive specificaions of he model. In order o check he adequacy of he model specificaion, we analyze he disurbances in he observable variables. If he model is correcly specified, he esimaed residuals for each observable variable are serially uncorrelaed and nearly uncorrelaed wih each oher. Thus, he residuals' sample auocorrelaion should be close o zero for observaions more han one period apar and ε should be a whie noise. We also use Brock, Decher, and Scheinkman s (987) BDS es for nonlinear models o check he i.i.d. assumpion for he disurbances. 5 The diagnosic ess for boh quarerly and monhly daa indicae ha he specificaions seleced are adequae for all equaions. The BDS es fails o rejec he i.i.d. hypohesis for he residuals. In addiion, he auocorrelaion funcions for he disurbances are wihin he limi of wo imes heir asympoic sandard deviaion, and he pairwise covariance beween he disurbances is nearly zero. We also es for he number of saes, as was done in Diebold and Rudebusch (996). In paricular, we employ he approach described in Garcia (992). Garcia shows ha if he ransiion probabiliies are reaed as nuisance parameers, resuls from Hansen (993, 996) 4 The exraced swiching facors are almos idenical for all specificaions when using he same variables. 5 For a vecor ε m = ε, ε+, ε+2,..., ε+m-, we use m=2,..., 5 and λ=sandard deviaion of ε, where λ is he disance beween any wo vecors, ε m and εs m. The es amouns o esimaing he probabiliy ha hese vecors are wihin he disance λ. 4

16 can be applied o es regime swiching models. 6 We consruc Garcia s es saisic and use criical values ha are repored in his paper. Alhough hese criical values are designed for an AR() regime swiching model and he es is parameer dependen, he highes value in Garcia s able for he % significance level is abou 2.5 imes smaller han he likelihood raio es for he dynamic facor wih regime swiching. 7 Hence, his es provides some evidence rejecing he one sae null hypohesis. We seleced he bes performing model for each daa frequency condiional on he resuls of he diagnosic ess. The quarerly specificaion, henceforh Model, is composed of he coinciden variables MTS, PILTP, ENAP and GDP. Boh he disurbances, v, and he facor, F, follow a second order auoregressive process in he ransiion equaions (b=2,f=2). For monhly ENAP, i is necessary o inroduce a high order auoregressive process o eliminae he misspecificaion in is equaion. Since his would amoun o sudying a lagging indicaor, we also examined oher alernaive measures of employmen such as NACE, TCE or HENAP. Parsimonious versions of he swiching dynamic facor model pass specificaion ess when we use hese coinciden variables. Thus, for he monhly analysis (Model 2), he series used are 6 Markov swiching models require non-sandard esing mehods since several of he classical assumpions of asympoic disribuion heory do no hold. For example, he ransiion probabiliies are no idenified under he null hypohesis, which implies ha he likelihood funcion wih respec o hem is fla a he opimum poin. Hansen (993, 996) proposes simulaion mehods o approximae he asympoic null disribuion of a sandardized likelihood es under non-sandard condiions. If he ransiion probabiliies are reaed as nuisance parameers, he asympoic one sae null disribuion is he supremum over all admissible values in he space of ransiion probabiliies. 7 We specify a grid in he space of he Markov parameers p and p22, where he range is from.2 o.95 in seps of.5. In order o overcome he problem of local maxima, we also esimaed he likelihood funcion under he alernaive using many differen ses of saring values. 5

17 MTS, PILTP, NACE and IP. A firs order auoregressive process was seleced for boh he disurbances and for he facor (b=,f=). Esimaion Resuls The quarerly daa are obained as simple averages of he monhly daa, which ends o smooh he series somewha. For monhly analysis, empirical models have no been as successful in exracing informaion abou flucuaions in economic aciviy, possibly because of noise inheren o he daa. For example, a univariae Markov swiching model, such as he one sudied in Hamilon (989), fails o accoun for several of he hisorical recessions when applied o some monhly coinciden variables. In addiion, according o Sock and Wason (993), heir monhly experimenal index gives only mild and delayed signals of he las recession and heir ou-of-sample esimaed probabiliies fail o forecas i. In conras wih he exising lieraure, he inferred probabiliies for monhly daa esimaed from he swiching dynamic facor model are highly correlaed wih NBER business cycle daing. In paricular, in an ou-of-sample exercise, he inferred probabiliies predic he las recession. The esimaes obained hrough numerical maximizaion of he condiional log likelihood funcion (2) are presened in Tables and 2, for quarerly and monhly daa, respecively. 8 The empirical resuls provide suppor o he Markov swiching framework. Boh monhly and quarerly samples are well characerized by he wo-sae specificaion. There is a significanly posiive growh rae in sae and a significanly negaive growh rae in sae 2. The asymmeries in he phases of he business cycle are also well characerized by he swiching dynamic facor. The esimaed ransiion probabiliies are subsanially 8 We also summarize he resuls of a more highly parameerized specificaion for he monhly frequency, alhough he specificaion ess favor more parsimonious versions. 6

18 significan and he probabiliy of saying in expansion, p, is higher han he probabiliy of saying in a conracion, p 22. This confirms previous findings ha he average duraion of recessions is smaller han he duraion of expansions. The expeced duraion for recession and expansion implied by he quarerly swiching models is, respecively, 5 and 3.7 quarers, compared o 4.4 and 4.3 quarers implied by he NBER daing echnique. 9 INSERT TABLES AND 2 Wih respec o he facor loadings, sales (MTS) and indusrial producion (IP) have he highes coefficiens and variances in boh models, supporing he observaion ha hey are he mos sensiive coinciden variables o business cycles. In fac, a hisorical examinaion of U.S. business cycles indicaes ha sales and producion respond immediaely and more inensively o changes in economic condiions close o urning poins han he oher variables analyzed. We also esimaed he model allowing he facor variance o be sae dependen. When he variance and he mean follow a Markov process, he asymmery in he daa is mosly absorbed by he variances. There is a low variance sae wih a high posiive mean, corresponding o he long and gradual expansions, and a high variance sae wih a posiive low mean, associaed wih seep and shor conracions. Probabiliies of Turning Poins The NBER s business cycle daing is generally recognized as he official chronology of urning poins. The deerminaion of peaks and roughs is he resul of a consensus among he Daing Commiee members, who each use differen procedures o examine business cycle phases. Various coinciden macroeconomic variables are examined and urning poins are chosen based on quasi-simulaneous accumulaion of inflecion poins. The subjecive aspec of k / ( ). k = The expeced duraion of recession is deermined by he formula: kp ( p ) = p 7

19 he NBER decision process may involve he use of differen crieria over ime, which suggess ha conclusions abou some feaures of expansions and conracions should be confroned wih alernaive daing mehodologies. 2 Anoher drawback of he NBER daing is ha decisions abou urning poins are released wih a long delay. In our case, inferences of he filered and smoohed probabiliies can be used o idenify peaks and roughs. Hence, our mehod allows for real ime assessmen of he economy and resuls can be consisenly reproduced. Figures and 3 graph he esimaed probabiliy ha he economy is in he recession sae a ime, based on informaion up o ime, Prob(S =2 I ), for Models and 2, respecively. Figures 2 and 4 repor he corresponding full sample smooher, Prob(S =2 I T ), for Models and 2. 2 The plos show ha he probabiliies of he recession sae are remarkably similar o he NBER daing of business cycles. All recessions are well characerized by boh filered and smoohed probabiliies, including he las recession of 99. For comparison, we also plo he smoohed probabiliies of a recession obained by fiing Hamilon s univariae model o monhly growh raes in indusrial producion, using an AR(8) process (Figure 5). 22 The inferred probabiliies are no srongly correlaed wih he NBER 2 Boldin (994) presens an exensive review and analysis of exising mehods for daing business cycle urning poins. 2 The bars in he figures represen hisorical recessions as deermined by he NBER. This informaion was no used in esimaing he model and is shown only for comparison wih he inferred probabiliies. The NBER business cycle daing is obained from Business Condiions Diges, June Alhough i may be appropriae o use 2 lags, o correspond o he four quarers in Hamilon s specificaion, he algorihm becomes compuaionally prohibiive for higher auoregressive processes. 8

20 daing of business cycle urning poins and hey fail o accoun for he 97, 982 and 99 recessions. 23 INSERT FIGURES TO 5 Table 3 repors recession urning poins derived from our smoohed probabiliies, using Hamilon s (989) crierion o characerize peaks and roughs. 24 Changes in he probabiliies rack very closely hisorical urning poins, and discrepancies wih he NBER daing are very small (no more han 2 periods), wih he excepion of he 957 and 99 recessions. For he 957 recession, he esimaed smoohed probabiliies for boh models indicae a peak before he official NBER dae. The probabiliies sugges, as also observed by Hamilon (989), ha he recession came as an immediae response o he oil price shock in he firs quarer of 957. In general, daing differences beween he proposed mehod and he NBER daing are concenraed in he deerminaion of peaks more han in roughs. In paricular, he roughs from Models and 2 almos all coincide wih he NBER s, wih he excepion of he las recession. INSERT TABLE 3 23 Hamilon s univariae Markov swiching model does no succeed in yielding resuls ha are srongly correlaed wih he NBER recession daing when applied o some coinciden macroeconomic variables, including monhly indusrial producion (IP), sales (MTS), personal income (PILTP), DOC coinciden indicaor (CCI) and employmen (ENAP). I is successful when applied o employmen (HENAP, NACE, TCE). The order of he assumed auoregressive process also affecs he resuls. 24 Under his mehod, he economy is in a recession if he full-sample smoohed probabiliy of recession is greaer han.5, Prob(S=2 IT)>.5. This meric is no necessarily opimal and flexibiliy should be considered in dubious cases, such as when he recession probabiliies are clusered in he inerval (.3,.7). We follow he NBER rule in considering he minimum duraion of a recession o be six monhs. 9

21 The economic recession in 99 exhibied some unusual feaures no observed in previous ones, in paricular during he final sage as he economy began o recover. Alhough, as in prior conracions, producion and sales had a seep upurn near he rough, real personal income recovered very slowly, and employmen remained low for a long ime afer he NBER declared he recession o be over in March Generally, a faser rise in employmen and income are observed during he recovery phase. This feaure is capured by he swiching dynamic facor srucure and is especially accenuaed in he model using quarerly daa, in which he probabiliies of recession decrease very slowly in he end of he 99 recession. In fac, for Model, he probabiliies indicae ha he recession did no end unil he firs quarer of According o he Bureau of Economic Analysis (BEA) official daing, which is based on he DOC coinciden indicaor, he rough occurred in January This is in close agreemen wih he findings from our exraced coinciden indicaor using quarerly daa. The inferred probabiliies are no only useful in idenifying he beginning and end of recessions as hey occur, bu hey also reveal momens of grea uncerainy in he economy. Almos all recessions were preceded by an increase in he recession probabiliies immediaely before i. Also, a mild rise in he probabiliies 5 o 2 monhs before a recession forewarns a subsequen downurn, wih he excepion of he 97 and 975 recessions. While i is he case ha no all recessions had hese prior indicaive spikes in he probabiliies, every ime here 25 The ensuing uncerainy in he economy during caused he NBER o delay is decision abou he rough of he recession for over a year. The rough in March 99 was chosen by he NBER based primarily on he recovery of indusrial producion, alhough a general rebound happened almos wo years laer. 26 Boldin (994), using a Markov swiching model for unemploymen o dae business cycle urning poins, finds ha an expansion did no begin unil mid Since his paper was compleed, he BEA, hrough exensive revisions of he series, changed he daing of he rough so ha i coincides wih he NBER daing. 2

22 was an abnormal change in he average expansion probabiliies, a recession followed beween half a year and a year laer. The mos noiceable spikes occurred in mid 956 and mid 959. These evens are no considered recessions due o heir very shor duraion of a mos a quarer. Thus, he swiching dynamic facor model migh be useful in capuring signals of an imminen recession ha are implici in coinciden macroeconomic variables. 28 Comparison wih he Deparmen of Commerce Indicaor The similariies beween he growh raes of he exraced facor and he Deparmen of Commerce coinciden indexes are sriking. As seen in Table 4, he growh raes of he exraced coinciden facors and he DOC indexes are highly correlaed for boh models. In paricular, he exraced facor and CCI growh raes for Model exhibi a correlaion of.96. The sandard deviaions of hese indexes are very close, differing by only percen. For Model 2, he correlaion of SFC wih CCI is.94. The SFC growh raes for boh models are ploed on Figures 6 and 7. INSERT TABLE 4 INSERT FIGURES 6 AND 7 28 The purpose of he coinciden indicaor is no o forecas business cycles, bu o obain real ime predicion of he sae of he economy and o dae urning poins. A leading indicaor would be a more appropriae ool for forecasing business condiions. 2

23 For graphical analysis i is easier o examine he indicaors in levels. 29 The level of he exraced index (SFC) for Models and 2, as well as he Composie Coinciden Index from he Deparmen of Commerce are ploed in Figures 8 and 9, respecively. For quarerly daa, he esimaed coinciden indicaor racks very closely he CCI index and, for almos he whole sample sudied, he wo series show he same paern regarding ampliude, iming and duraion of flucuaions. The ime series for he monhly SFC and CCI in levels are also very similar wih respec o he iming and duraion of he cycles, alhough he esimaed coinciden index exhibis more accenuaed oscillaions. INSERT FIGURES 8 AND 9 For he 99 recession, he exraced SFC indicaors for boh models show a deeper decline han he CCI. A possible reason for his is relaed o he weigh of each coinciden variable in he index consrucion. The Deparmen of Commerce calculaes is coinciden index as a weighed average of individual componens, where he weighs are inversely relaed o he series esimaed volailiy. This implies, for example, ha employmen and personal income receive he highes weigh in he consrucion of CCI. In our model, we do no place any a priori resricions on he weighs assigned o each variable ha eners our coinciden indicaor. As i urns ou, he mos volaile variables, sales and producion, are he ones more highly correlaed o he exraced coinciden index, alhough employmen and personal income also 29 We use he ideniy F - = F - +F -2 in he nonlinear filer o obain he facor level, FL, where F - =*log(fl - ). From he esimaed resuls, he exraced facor in levels is obained by exponeniaing.*f-. The Deparmen of Commerce calculaes he coinciden index as a weighed average of is individual componens, CCI, ha is: n CCI = i bi Yi, +, where, bi are he weighs, Yi are he growh rae of he coinciden variables and (=-3% a = monh) is an adjusmen so ha he index has he same rend as GDP. For graphical comparison, we also accoun for he rend adjusmen imposed on he calculaion of he DOC coinciden index. 22

24 play an imporan role. The more volaile series are he ones ha displayed a seeper decline during he las recession, which migh accoun for he difference beween our coinciden indicaor and he DOC index. The slow recovery following he 99 recession is capured by our SFC index and he Deparmen of Commerce indicaor, boh of which indicae an economic conracion lasing unil he beginning of 992. The monhly SFC index shows a shorer recession in 99 han he quarerly exraced index. This migh be caused by he faser recovery of he monhly IP in he firs quarer of 99. This is he variable wih he highes esimaed weigh in our monhly coinciden indicaor. Figure shows he CCI and he monhly index obained by Sock and Wason (99). Sock and Wason s index has a sandard deviaion 8% smaller han he CCI index. Thus, any comparison of hese wo measures involves an exra correcion. 3 The SW index is more jagged, has a smaller mean han he CCI, and underpredics i for he whole sample period. Wih respec o he 99 recession, he SW index provides weak and lae signals of a recession exhibiing a fas revival a a ime when he economy was sill in a slow recovery as indicaed by he CCI index. Our exraced swiching facor series, as seen in Figures 8 and 9, capures in a imely manner he las recession as well as he slow recovery. INSERT FIGURE 5. OUT-OF-SAMPLE PERFORMANCE - THE 99 RECESSION We examine he performance of inferred probabiliies in predicing urning poins in an ou-of-sample exercise. The probabiliy forecass are evaluaed wih respec o heir accuracy 3 Sock and Wason (99) use a modified facor growh rae o exrac he level, whose sandard deviaion is se o he same value as he DOC coinciden index and is mean is kep he same. The series is hen scaled o equal in July

25 and calibraion in predicing observed realizaions by using he quadraic probabiliy score (QPS), he raw correlaion, and he global square bias (GSB), for boh he NBER and he BEA daing. 3 Two ses of pos-sample daa are examined: hisorically revised daa as well as parially revised or real ime daa. The idea is o compare and evaluae no only he model performance of ex-pos forecass, bu also real ime ex-ane forecass using only daa available a he ime of forecasing. As discussed in Diebold and Rudebusch (99), since macroeconomic series undergo several revisions and definiional changes over ime, he use of real ime daa in an ou-of-sample exercise provides a more rigorous es of model performance for ex-ane forecass. The parameers were esimaed using daa up o 989.4, for quarerly daa, and up o 989.2, for monhly daa. The in-sample esimaes were hen used o generae ou-of-sample forecass of he filered probabiliies. For quarerly analysis, ou-of-sample performance is analyzed from 99. hrough 993. and for monhly, from 99. hrough Given he sample selecion, he ou-of-sample exercise amouns o esing he model for a very unusual period corresponding o he economic downurn in 99 and he sluggish recovery of he economy in The dynamic facor models wih regime swiching successfully characerize he las recession using boh filered and smoohed probabiliies and for boh quarerly and monhly daa. The monhly model yields daing of urning poins closer o he NBER while he quarerly model is more in accord wih he BEA daing. Ex-Pos Performance - Revised Daa 2 3 The quadraic probabiliy score and he global square bias are, respecively: QPS = T T and GSB = 2{ {Prob[S = 2 I ] - T T = = N } Prob[S=2 I] are he filered probabiliies of recession. T 2 T = {Prob[S = 2 I ] - N }, where N is he / dummy for he NBER or BEA recessions and τ 2, 24

26 Table 5 repors he ou-of-sample performance of he probabiliies in forecasing urning poins. The dynamic facor model displays a slighly beer pos sample performance in erms of he QPS for regime forecass han he in-sample resuls. Also, he proposed model shows beer ou-of-sample performance in erms of he QPS for he NBER regime forecass when compared o alernaive models. The QPS obained for Models and 2 are, respecively,.29 and.. These values are smaller, for example, han he QPS=.34 obained by Hamilon and Perez-Quiros (996) for a bivariae Markov Swiching VAR of he DOC leading indicaor and GNP. In fac, he inferred probabiliies from heir model miss he 99 recession. In he middle of he recession, heir inferred probabiliies of a recession were no greaer han 25%. INSERT TABLE 5 The uncerainy in he pah of he economy during is also capured by he ou-ofsample filered probabiliies obained from boh Models and 2, bu i is paricularly accenuaed for he quarerly frequency (Figure ). 32 A graphical comparison of he ou-ofsample filered probabiliies for Model and he DOC Coinciden Indicaor (Figure ) shows ha he probabiliies of recession characerize he economy in a very similar way as he CCI. The rough deermined by he NBER o be in he firs quarer of 99 corresponds o a period of flaness in he CCI. I also coincides wih he momen in which he probabiliies of recession sar decreasing. However, hese probabiliies decrease very slowly during he firs and second quarer of 99, and increase again in he hird quarer when he CCI also shows a decline. Only in he firs quarer of 992 did he probabiliies fall below 5%, indicaing he end of he recession. This is in closer agreemen wih he rough decided by he BEA. The QPS 32 This difference migh be explained by he fac ha he monhly model uses he variable IP, which showed a seep upurn in March 99. The variable GDP, used in he quarerly model, shows a mild increase in he firs hree quarers of 99 and a seeper rebound only in he las quarer. 25

27 measuring he closeness of he filered probabiliies o he BEA daing is only.78, and he GSB=.39. INSERT FIGURE Real Time Analysis Ou-of-sample performance is examined wih real ime monhly daa available a he dae of each forecas, obained from he Survey of Curren Business. 33 Table 5 repors he ou-ofsample performance for monhly daa, using our real ime daa se. Model 2 performs well in erms of forecasing he NBER regimes, achieving a QPS=.6, a GSB=.3 and a raw correlaion beween he filered probabiliies and he NBER business cycle daes of.6. Figures 2 and 3 show he filered probabiliies of recession for revised and real ime monhly daa. The probabiliies using real ime daa are more volaile, reflecing he uncerainy of he economy during he period. In he beginning of 99 he probabiliy of a recession had a shor and pronounced increase o.8, indicaing he subsequen economic conracion. The probabiliies were above 5% again in May 99. Tha is, he swiching facor model indicaes an economic downurn a he same ime he economy was signaling a recession, using only daa available hen. The model also forecass he beginning of he recession before i occurred. The one-sep ahead probabiliy of a recession, based on real ime daa up o May, signals a 5.4% chance of a recession in June (Figure 4). The zero-sep ahead probabiliy forecass idenify he end of he recession in March 99. These probabiliies also indicae uncerainy in he economy a he end of 99, increasing close o he 5% level a he 33 Real ime dae corresponds o daa released a +2. For example, daa for January 99 was obained from he March 99 issue of he Survey of Curren Business. This daa selecion is based on Diebold and Rudebusch s (99) evidence ha using preliminary and incomplee daa, as released a +, leads o a poor forecasing performance. 26

28 ime sales and indusrial producion showed a modes decline. INSERT FIGURES 2 AND 3 According o Sock and Wason (993), heir experimenal index fails o characerize and forecas he las recession. Their ou-of-sample esimaed probabiliies signal a recession only in November of 99. In Ocober, a quarer afer he beginning of he recession, he zero-sep ahead recession probabiliy was only.28. The hree-monh ahead probabiliy forecas was.23 in November, based on informaion up o Augus, and he one-sep ahead probabiliy of a recession was.5 in boh May and in June, failing o forecas he las recession. 6. SUMMARY AND CONCLUDING REMARKS This paper proposes a model in which business cycles are empirically characerized by a dynamic facor wih regime swiches. The approach capures boh he idea of business cycles as comovemens in several macroeconomic variables and he asymmeric naure of business cycle phases. The opimally inferred daes of business cycle urning poins display a srong correlaion wih he NBER daing of business cycles and he exraced dynamic facor is remarkably similar o he Deparmen of Commerce coinciden indicaor. In paricular, he resuls highligh he imporance of nonlineariies in business cycles. The model provides a more rigorous and imely approach for daing business cycle urning poins han radiional mehods. In paricular, our approach is based on a probabilisic framework ha can be used in real ime o assess he sae of he economy and ha can be replicaed consisenly a any ime. The resuls sugges ha a very saisfacory represenaion of he sample daa is obained by modeling business cycles as he common elemen underlying a se of coinciden variables subjec o sporadic regime shifs. The proposed framework is also a useful ool for ex-ane predicion of business cycle urning poins. Invesigaion using boh revised daa and 27

29 informaion available o agens in real ime indicaes ha he exraced coinciden index and esimaed probabiliies perform very well in heir abiliy o characerize hese urning poins. In he fuure, i migh be worhwhile o invesigae wheher exending he approach in his paper o include leading macroeconomic variables migh yield a leading indicaor ha could be successfully used o forecas urning poins. Also, including addiional saes in he Markov sochasic process migh improve he performance of he model. For example, Burns and Michell (946) conceive business cycles as composed of four disinc periods: prosperiy, crisis, depression and revivals. I migh be ineresing o invesigae his noion using he framework sudied in his paper. In closing, le us address he relaionship of his paper o he conemporaneous and independen work of Kim and Yoo (995). Alhough he Kim-Yoo approach is similar o ours, here are imporan differences, relaed o choice of sample period, model specificaion, and he variables used. As regards sample period, he Kim-Yoo sample sars in 96, which excludes wo recessions compared o our sample daa. Thus, our esimaion uses informaion obained from 8 recessions, while heirs uses informaion from 6 recessions. As regards model specificaion and he variables used, Kim and Yoo use he ENAP employmen variable, which according o Sock and Wason (99) requires exra lags in is equaion o avoid model misspecificaion. This resuls in a mixed coinciden/lagging index specificaion, which is unforunae given ha he objecive is o consruc a coinciden index model. As was discussed in Secion 4, we obain a beer-specified version of he swiching dynamic facor model by using he employmen series NACE insead of ENAP. The upsho is simply ha, because of differences in sample period, model specificaion, and he variables used, he Kim-Yoo coinciden indicaor behaves very differenly from ours. The Kim-Yoo coinciden indicaor is highly correlaed wih Sock and Wason's (he correlaion 28

Vector Autoregressions (VARs): Operational Perspectives

Vector Autoregressions (VARs): Operational Perspectives Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101-115. Macroeconomericians

More information

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of Prof. Harris Dellas Advanced Macroeconomics Winer 2001/01 The Real Business Cycle paradigm The RBC model emphasizes supply (echnology) disurbances as he main source of macroeconomic flucuaions in a world

More information

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005 FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970-005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a

More information

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.

More information

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he

More information

Multiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States

Multiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States Deparmen of Economics Discussion Paper 00-07 Muliple Srucural Breaks in he Nominal Ineres Rae and Inflaion in Canada and he Unied Saes Frank J. Akins, Universiy of Calgary Preliminary Draf February, 00

More information

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios

More information

Cointegration: The Engle and Granger approach

Cointegration: The Engle and Granger approach Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry

More information

The naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1

The naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1 Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces ime-series smoohing forecasing mehods. Various models are discussed,

More information

House Price Index (HPI)

House Price Index (HPI) House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales

More information

Issues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d

Issues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d These noes largely concern auocorrelaion Issues Using OLS wih Time Series Daa Recall main poins from Chaper 10: Time series daa NOT randomly sampled in same way as cross secional each obs no i.i.d Why?

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal Of Business & Economics Research September 2005 Volume 3, Number 9 Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

More information

The Relationship between Stock Return Volatility and. Trading Volume: The case of The Philippines*

The Relationship between Stock Return Volatility and. Trading Volume: The case of The Philippines* The Relaionship beween Sock Reurn Volailiy and Trading Volume: The case of The Philippines* Manabu Asai Faculy of Economics Soka Universiy Angelo Unie Economics Deparmen De La Salle Universiy Manila May

More information

Revisions to Nonfarm Payroll Employment: 1964 to 2011

Revisions to Nonfarm Payroll Employment: 1964 to 2011 Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm

More information

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,

More information

DEMAND FORECASTING MODELS

DEMAND FORECASTING MODELS DEMAND FORECASTING MODELS Conens E-2. ELECTRIC BILLED SALES AND CUSTOMER COUNTS Sysem-level Model Couny-level Model Easside King Couny-level Model E-6. ELECTRIC PEAK HOUR LOAD FORECASTING Sysem-level Forecas

More information

SEASONAL ADJUSTMENT. 1 Introduction. 2 Methodology. 3 X-11-ARIMA and X-12-ARIMA Methods

SEASONAL ADJUSTMENT. 1 Introduction. 2 Methodology. 3 X-11-ARIMA and X-12-ARIMA Methods SEASONAL ADJUSTMENT 1 Inroducion 2 Mehodology 2.1 Time Series and Is Componens 2.1.1 Seasonaliy 2.1.2 Trend-Cycle 2.1.3 Irregulariy 2.1.4 Trading Day and Fesival Effecs 3 X-11-ARIMA and X-12-ARIMA Mehods

More information

Why Did the Demand for Cash Decrease Recently in Korea?

Why Did the Demand for Cash Decrease Recently in Korea? Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in

More information

Price elasticity of demand for crude oil: estimates for 23 countries

Price elasticity of demand for crude oil: estimates for 23 countries Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

More information

Forecasting Malaysian Gold Using. GARCH Model

Forecasting Malaysian Gold Using. GARCH Model Applied Mahemaical Sciences, Vol. 7, 2013, no. 58, 2879-2884 HIKARI Ld, www.m-hikari.com Forecasing Malaysian Gold Using GARCH Model Pung Yean Ping 1, Nor Hamizah Miswan 2 and Maizah Hura Ahmad 3 Deparmen

More information

II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal

II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

JEL classifications: Q43;E44 Keywords: Oil shocks, Stock market reaction.

JEL classifications: Q43;E44 Keywords: Oil shocks, Stock market reaction. Applied Economerics and Inernaional Developmen. AEID.Vol. 5-3 (5) EFFECT OF OIL PRICE SHOCKS IN THE U.S. FOR 1985-4 USING VAR, MIXED DYNAMIC AND GRANGER CAUSALITY APPROACHES AL-RJOUB, Samer AM * Absrac

More information

Chapter 8 Student Lecture Notes 8-1

Chapter 8 Student Lecture Notes 8-1 Chaper Suden Lecure Noes - Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing -Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop

More information

NON-PARAMETRIC AND PARAMETRIC APPROACHES TO THE CZECH BUSINESS CYCLE DATING

NON-PARAMETRIC AND PARAMETRIC APPROACHES TO THE CZECH BUSINESS CYCLE DATING NON-PARAMETRIC AND PARAMETRIC APPROACHES TO THE CZECH BUSINESS CYCLE DATING LENKA VRANÁ Universiy of Economics, Prague, Faculy of Informaics and Saisics, Deparmen of Saisics and Probabiliy W. Churchill

More information

Time Series Analysis Using SAS R Part I The Augmented Dickey-Fuller (ADF) Test

Time Series Analysis Using SAS R Part I The Augmented Dickey-Fuller (ADF) Test ABSTRACT Time Series Analysis Using SAS R Par I The Augmened Dickey-Fuller (ADF) Tes By Ismail E. Mohamed The purpose of his series of aricles is o discuss SAS programming echniques specifically designed

More information

GOOD NEWS, BAD NEWS AND GARCH EFFECTS IN STOCK RETURN DATA

GOOD NEWS, BAD NEWS AND GARCH EFFECTS IN STOCK RETURN DATA Journal of Applied Economics, Vol. IV, No. (Nov 001), 313-37 GOOD NEWS, BAD NEWS AND GARCH EFFECTS 313 GOOD NEWS, BAD NEWS AND GARCH EFFECTS IN STOCK RETURN DATA CRAIG A. DEPKEN II * The Universiy of Texas

More information

Supplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect Risk-Taking?

Supplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect Risk-Taking? Supplemenary Appendix for Depression Babies: Do Macroeconomic Experiences Affec Risk-Taking? Ulrike Malmendier UC Berkeley and NBER Sefan Nagel Sanford Universiy and NBER Sepember 2009 A. Deails on SCF

More information

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper

More information

Bid-ask Spread and Order Size in the Foreign Exchange Market: An Empirical Investigation

Bid-ask Spread and Order Size in the Foreign Exchange Market: An Empirical Investigation Bid-ask Spread and Order Size in he Foreign Exchange Marke: An Empirical Invesigaion Liang Ding* Deparmen of Economics, Macaleser College, 1600 Grand Avenue, S. Paul, MN55105, U.S.A. Shor Tile: Bid-ask

More information

APPLICATION OF THE KALMAN FILTER FOR ESTIMATING CONTINUOUS TIME TERM STRUCTURE MODELS: THE CASE OF UK AND GERMANY. January, 2005

APPLICATION OF THE KALMAN FILTER FOR ESTIMATING CONTINUOUS TIME TERM STRUCTURE MODELS: THE CASE OF UK AND GERMANY. January, 2005 APPLICATION OF THE KALMAN FILTER FOR ESTIMATING CONTINUOUS TIME TERM STRUCTURE MODELS: THE CASE OF UK AND GERMANY Somnah Chaeree* Deparmen of Economics Universiy of Glasgow January, 2005 Absrac The purpose

More information

Usefulness of the Forward Curve in Forecasting Oil Prices

Usefulness of the Forward Curve in Forecasting Oil Prices Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,

More information

SPECIAL REPORT May 4, Shifting Drivers of Inflation Canada versus the U.S.

SPECIAL REPORT May 4, Shifting Drivers of Inflation Canada versus the U.S. Paul Ferley Assisan Chief Economis 416-974-7231 paul.ferley@rbc.com Nahan Janzen Economis 416-974-0579 nahan.janzen@rbc.com SPECIAL REPORT May 4, 2010 Shifing Drivers of Inflaion Canada versus he U.S.

More information

A PROPOSAL TO OBTAIN A LONG QUARTERLY CHILEAN GDP SERIES *

A PROPOSAL TO OBTAIN A LONG QUARTERLY CHILEAN GDP SERIES * CUADERNOS DE ECONOMÍA, VOL. 43 (NOVIEMBRE), PP. 285-299, 2006 A PROPOSAL TO OBTAIN A LONG QUARTERLY CHILEAN GDP SERIES * JUAN DE DIOS TENA Universidad de Concepción y Universidad Carlos III, España MIGUEL

More information

Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach * Ben S. Bernanke, Federal Reserve Board

Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach * Ben S. Bernanke, Federal Reserve Board Measuring he Effecs of Moneary Policy: A acor-augmened Vecor Auoregressive (AVAR) Approach * Ben S. Bernanke, ederal Reserve Board Jean Boivin, Columbia Universiy and NBER Pior Eliasz, Princeon Universiy

More information

Appendix D Flexibility Factor/Margin of Choice Desktop Research

Appendix D Flexibility Factor/Margin of Choice Desktop Research Appendix D Flexibiliy Facor/Margin of Choice Deskop Research Cheshire Eas Council Cheshire Eas Employmen Land Review Conens D1 Flexibiliy Facor/Margin of Choice Deskop Research 2 Final Ocober 2012 \\GLOBAL.ARUP.COM\EUROPE\MANCHESTER\JOBS\200000\223489-00\4

More information

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

More information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

Price Controls and Banking in Emissions Trading: An Experimental Evaluation

Price Controls and Banking in Emissions Trading: An Experimental Evaluation This version: March 2014 Price Conrols and Banking in Emissions Trading: An Experimenal Evaluaion John K. Sranlund Deparmen of Resource Economics Universiy of Massachuses-Amhers James J. Murphy Deparmen

More information

Risk Modelling of Collateralised Lending

Risk Modelling of Collateralised Lending Risk Modelling of Collaeralised Lending Dae: 4-11-2008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies

More information

ON THURSTONE'S MODEL FOR PAIRED COMPARISONS AND RANKING DATA

ON THURSTONE'S MODEL FOR PAIRED COMPARISONS AND RANKING DATA ON THUSTONE'S MODEL FO PAIED COMPAISONS AND ANKING DATA Alber Maydeu-Olivares Dep. of Psychology. Universiy of Barcelona. Paseo Valle de Hebrón, 171. 08035 Barcelona (Spain). Summary. We invesigae by means

More information

The Asymmetric Effects of Oil Shocks on an Oil-exporting Economy*

The Asymmetric Effects of Oil Shocks on an Oil-exporting Economy* CUADERNOS DE ECONOMÍA, VOL. 47 (MAYO), PP. 3-13, 2010 The Asymmeric Effecs of Oil Shocks on an Oil-exporing Economy* Omar Mendoza Cenral Bank of Venezuela David Vera Ken Sae Universiy We esimae he effecs

More information

Term Structure of Prices of Asian Options

Term Structure of Prices of Asian Options Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:

More information

CAUSAL RELATIONSHIP BETWEEN STOCK MARKET AND EXCHANGE RATE, FOREIGN EXCHANGE RESERVES AND VALUE OF TRADE BALANCE: A CASE STUDY FOR INDIA

CAUSAL RELATIONSHIP BETWEEN STOCK MARKET AND EXCHANGE RATE, FOREIGN EXCHANGE RESERVES AND VALUE OF TRADE BALANCE: A CASE STUDY FOR INDIA CAUSAL RELATIONSHIP BETWEEN STOCK MARKET AND EXCHANGE RATE, FOREIGN EXCHANGE RESERVES AND VALUE OF TRADE BALANCE: A CASE STUDY FOR INDIA BASABI BHATTACHARYA & JAYDEEP MUKHERJEE Reader, Deparmen of Economics,

More information

Consumer sentiment is arguably the

Consumer sentiment is arguably the Does Consumer Senimen Predic Regional Consumpion? Thomas A. Garre, Rubén Hernández-Murillo, and Michael T. Owyang This paper ess he abiliy of consumer senimen o predic reail spending a he sae level. The

More information

Estimating Time-Varying Equity Risk Premium The Japanese Stock Market 1980-2012

Estimating Time-Varying Equity Risk Premium The Japanese Stock Market 1980-2012 Norhfield Asia Research Seminar Hong Kong, November 19, 2013 Esimaing Time-Varying Equiy Risk Premium The Japanese Sock Marke 1980-2012 Ibboson Associaes Japan Presiden Kasunari Yamaguchi, PhD/CFA/CMA

More information

ARCH 2013.1 Proceedings

ARCH 2013.1 Proceedings Aricle from: ARCH 213.1 Proceedings Augus 1-4, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference

More information

Part 1: White Noise and Moving Average Models

Part 1: White Noise and Moving Average Models Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical

More information

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were

More information

Investor sentiment of lottery stock evidence from the Taiwan stock market

Investor sentiment of lottery stock evidence from the Taiwan stock market Invesmen Managemen and Financial Innovaions Volume 9 Issue 1 Yu-Min Wang (Taiwan) Chun-An Li (Taiwan) Chia-Fei Lin (Taiwan) Invesor senimen of loery sock evidence from he Taiwan sock marke Absrac This

More information

Information Theoretic Approaches for Predictive Models: Results and Analysis

Information Theoretic Approaches for Predictive Models: Results and Analysis Informaion Theoreic Approaches for Predicive Models: Resuls and Analysis Monica Dinculescu Supervised by Doina Precup Absrac Learning he inernal represenaion of parially observable environmens has proven

More information

Chapter 6: Business Valuation (Income Approach)

Chapter 6: Business Valuation (Income Approach) Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he

More information

Modelling the dependence of the UK stock market on the US stock market: A need for multiple regimes

Modelling the dependence of the UK stock market on the US stock market: A need for multiple regimes Modelling he dependence of he UK sock marke on he US sock marke: A need for muliple regimes A J Khadaroo Deparmen of Economics and Saisics Universiy of Mauriius Redui Mauriius Email: j.khadaroo@uom.ac.mu

More information

The Transport Equation

The Transport Equation The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

More information

Machine Learning in Pairs Trading Strategies

Machine Learning in Pairs Trading Strategies Machine Learning in Pairs Trading Sraegies Yuxing Chen (Joseph) Deparmen of Saisics Sanford Universiy Email: osephc5@sanford.edu Weiluo Ren (David) Deparmen of Mahemaics Sanford Universiy Email: weiluo@sanford.edu

More information

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C.

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. The Effecs of Unemploymen Benefis on Unemploymen and Labor Force Paricipaion:

More information

ANALYSIS OF ECONOMIC CYCLES USING UNOBSERVED COMPONENTS MODELS

ANALYSIS OF ECONOMIC CYCLES USING UNOBSERVED COMPONENTS MODELS ANALYSIS OF ECONOMIC CYCLES USING UNOBSERVED COMPONENTS MODELS Diego J. Pedregal Escuela Técnica Superior de Ingenieros Indusriales Universidad de Casilla-La Mancha Avda. Camilo José Cela, 3 13071 Ciudad

More information

Oil Price Fluctuations and Firm Performance in an Emerging Market: Assessing Volatility and Asymmetric Effect

Oil Price Fluctuations and Firm Performance in an Emerging Market: Assessing Volatility and Asymmetric Effect Journal of Economics, Business and Managemen, Vol., No. 4, November 203 Oil Price Flucuaions and Firm Performance in an Emerging Marke: Assessing Volailiy and Asymmeric Effec Hawai Janor, Aisyah Abdul-Rahman,

More information

THE NEW MARKET EFFECT ON RETURN AND VOLATILITY OF SPANISH STOCK SECTOR INDEXES

THE NEW MARKET EFFECT ON RETURN AND VOLATILITY OF SPANISH STOCK SECTOR INDEXES THE NEW MARKET EFFECT ON RETURN AND VOLATILITY OF SPANISH STOCK SECTOR INDEXES Juan Ángel Lafuene Universidad Jaume I Unidad Predeparamenal de Finanzas y Conabilidad Campus del Riu Sec. 1080, Casellón

More information

Premium Income of Indian Life Insurance Industry

Premium Income of Indian Life Insurance Industry Premium Income of Indian Life Insurance Indusry A Toal Facor Produciviy Approach Ram Praap Sinha* Subsequen o he passage of he Insurance Regulaory and Developmen Auhoriy (IRDA) Ac, 1999, he life insurance

More information

Stochastic Optimal Control Problem for Life Insurance

Stochastic Optimal Control Problem for Life Insurance Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian

More information

The Application of Multi Shifts and Break Windows in Employees Scheduling

The Application of Multi Shifts and Break Windows in Employees Scheduling The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

Occasional Paper series

Occasional Paper series Occasional Paper series No 84 / Shor-erm forecasing of GDP using large monhly daases a pseudo real-ime forecas evaluaion exercise by Karim Barhoumi, Szilard Benk, Riccardo Crisadoro, Ard Den Reijer, Audronė

More information

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand 36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,

More information

A New Indicator Based on Neftçi s Approach for Predicting Turning Points of the Euro-Zone Growth Cycle*

A New Indicator Based on Neftçi s Approach for Predicting Turning Points of the Euro-Zone Growth Cycle* Viereljahrshefe zur Wirschafsforschung 7. Jahrgang, Hef 3/2 S. 364 376 A ew Indicaor Based on efçi s Approach for Predicing Turning Poins of he Euro-Zone Growh Cycle* By Jacques Anas and Muriel guiffo-boyom**

More information

MALAYSIAN FOREIGN DIRECT INVESTMENT AND GROWTH: DOES STABILITY MATTER? Jarita Duasa 1

MALAYSIAN FOREIGN DIRECT INVESTMENT AND GROWTH: DOES STABILITY MATTER? Jarita Duasa 1 Journal of Economic Cooperaion, 8, (007), 83-98 MALAYSIAN FOREIGN DIRECT INVESTMENT AND GROWTH: DOES STABILITY MATTER? Jaria Duasa 1 The objecive of he paper is wofold. Firs, is o examine causal relaionship

More information

INTRODUCTION TO FORECASTING

INTRODUCTION TO FORECASTING INTRODUCTION TO FORECASTING INTRODUCTION: Wha is a forecas? Why do managers need o forecas? A forecas is an esimae of uncerain fuure evens (lierally, o "cas forward" by exrapolaing from pas and curren

More information

Influence of the Dow returns on the intraday Spanish stock market behavior

Influence of the Dow returns on the intraday Spanish stock market behavior Influence of he Dow reurns on he inraday Spanish sock marke behavior José Luis Miralles Marcelo, José Luis Miralles Quirós, María del Mar Miralles Quirós Deparmen of Financial Economics, Universiy of Exremadura

More information

DYNAMIC ECONOMETRIC MODELS Vol. 7 Nicolaus Copernicus University Toruń 2006. Ryszard Doman Adam Mickiewicz University in Poznań

DYNAMIC ECONOMETRIC MODELS Vol. 7 Nicolaus Copernicus University Toruń 2006. Ryszard Doman Adam Mickiewicz University in Poznań DYNAMIC ECONOMETRIC MODELS Vol. 7 Nicolaus Copernicus Universiy Toruń 26 1. Inroducion Adam Mickiewicz Universiy in Poznań Measuring Condiional Dependence of Polish Financial Reurns Idenificaion of condiional

More information

Lead Lag Relationships between Futures and Spot Prices

Lead Lag Relationships between Futures and Spot Prices Working Paper No. 2/02 Lead Lag Relaionships beween Fuures and Spo Prices by Frank Asche Ale G. Guormsen SNF-projec No. 7220: Gassmarkeder, menneskelig kapial og selskapssraegier The projec is financed

More information

Why does the correlation between stock and bond returns vary over time?

Why does the correlation between stock and bond returns vary over time? Why does he correlaion beween sock and bond reurns vary over ime? Magnus Andersson a,*, Elizavea Krylova b,**, Sami Vähämaa c,*** a European Cenral Bank, Capial Markes and Financial Srucure Division b

More information

Statistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by Song-Hee Kim and Ward Whitt

Statistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by Song-Hee Kim and Ward Whitt Saisical Analysis wih Lile s Law Supplemenary Maerial: More on he Call Cener Daa by Song-Hee Kim and Ward Whi Deparmen of Indusrial Engineering and Operaions Research Columbia Universiy, New York, NY 17-99

More information

The Maturity Structure of Volatility and Trading Activity in the KOSPI200 Futures Market

The Maturity Structure of Volatility and Trading Activity in the KOSPI200 Futures Market The Mauriy Srucure of Volailiy and Trading Aciviy in he KOSPI200 Fuures Marke Jong In Yoon Division of Business and Commerce Baekseok Univerisy Republic of Korea Email: jiyoon@bu.ac.kr Received Sepember

More information

Estimating the Term Structure with Macro Dynamics in a Small Open Economy

Estimating the Term Structure with Macro Dynamics in a Small Open Economy Esimaing he Term Srucure wih Macro Dynamics in a Small Open Economy Fousseni Chabi-Yo Bank of Canada Jun Yang Bank of Canada April 18, 2006 Preliminary work. Please do no quoe wihou permission. The paper

More information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer) Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions

More information

Small and Large Trades Around Earnings Announcements: Does Trading Behavior Explain Post-Earnings-Announcement Drift?

Small and Large Trades Around Earnings Announcements: Does Trading Behavior Explain Post-Earnings-Announcement Drift? Small and Large Trades Around Earnings Announcemens: Does Trading Behavior Explain Pos-Earnings-Announcemen Drif? Devin Shanhikumar * Firs Draf: Ocober, 2002 This Version: Augus 19, 2004 Absrac This paper

More information

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

More information

A Note on the Impact of Options on Stock Return Volatility. Nicolas P.B. Bollen

A Note on the Impact of Options on Stock Return Volatility. Nicolas P.B. Bollen A Noe on he Impac of Opions on Sock Reurn Volailiy Nicolas P.B. Bollen ABSTRACT This paper measures he impac of opion inroducions on he reurn variance of underlying socks. Pas research generally finds

More information

Implied Equity Duration: A New Measure of Equity Risk *

Implied Equity Duration: A New Measure of Equity Risk * Implied Equiy Duraion: A New Measure of Equiy Risk * Paricia M. Dechow The Carleon H. Griffin Deloie & Touche LLP Collegiae Professor of Accouning, Universiy of Michigan Business School Richard G. Sloan

More information

Hiring as Investment Behavior

Hiring as Investment Behavior Review of Economic Dynamics 3, 486522 Ž 2000. doi:10.1006redy.1999.0084, available online a hp:www.idealibrary.com on Hiring as Invesmen Behavior Eran Yashiv 1 The Eian Berglas School of Economics, Tel

More information

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se

More information

Predicting Stock Market Index Trading Signals Using Neural Networks

Predicting Stock Market Index Trading Signals Using Neural Networks Predicing Sock Marke Index Trading Using Neural Neworks C. D. Tilakarane, S. A. Morris, M. A. Mammadov, C. P. Hurs Cenre for Informaics and Applied Opimizaion School of Informaion Technology and Mahemaical

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

THE RELATIONSHIPS AMONG PETROLEUM PRICES. Abstract

THE RELATIONSHIPS AMONG PETROLEUM PRICES. Abstract Inernaional Conference On Applied Economics ICOAE 2010 459 THE RELATIONSHIPS AMONG PETROLEUM PRICES RAYMOND LI 1 Absrac This paper evaluaes in a mulivariae framework he relaionship among he spo prices

More information

Maccini, Louis J.; Schaller, Huntley; Moore, Bartholomew. Working Papers, The Johns Hopkins University, Department of Economics, No.

Maccini, Louis J.; Schaller, Huntley; Moore, Bartholomew. Working Papers, The Johns Hopkins University, Department of Economics, No. econsor www.econsor.eu Der Open-Access-Publikaionsserver der ZBW Leibniz-Informaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics Maccini, Louis J.;

More information

An Economic Indicator for the State of the Economy in the Southeastern U.S.

An Economic Indicator for the State of the Economy in the Southeastern U.S. JRAP 42(1): 1-27. 2012 MCRSA. All righs reserved. An Economic Indicaor for he Sae of he Economy in he Souheasern U.S. Tom W. Miller and Donald Sabbarese Kennesaw Sae Universiy USA Absrac. A sae space model

More information

The High Yield Spread as a Predictor of Real Economic Activity: Evidence of a Financial Accelerator for the United States

The High Yield Spread as a Predictor of Real Economic Activity: Evidence of a Financial Accelerator for the United States The High Yield Spread as a Predicor of Real Economic Aciviy: Evidence of a Financial Acceleraor for he Unied Saes Ashoa Mody Research Deparmen Inernaional Moneary Fund Mar P. Taylor Universiy of Warwic

More information

Diane K. Michelson, SAS Institute Inc, Cary, NC Annie Dudley Zangi, SAS Institute Inc, Cary, NC

Diane K. Michelson, SAS Institute Inc, Cary, NC Annie Dudley Zangi, SAS Institute Inc, Cary, NC ABSTRACT Paper DK-02 SPC Daa Visualizaion of Seasonal and Financial Daa Using JMP Diane K. Michelson, SAS Insiue Inc, Cary, NC Annie Dudley Zangi, SAS Insiue Inc, Cary, NC JMP Sofware offers many ypes

More information

Time-Varying Effect of Oil Market Shocks on the Stock Market

Time-Varying Effect of Oil Market Shocks on the Stock Market Crawford School of Public Policy CAMA Cenre for Applied Macroeconomic Analysis Time-Varying Effec of Oil Marke Shocks on he Sock Marke CAMA Working Paper 35/2015 Augus 2015 Wensheng Kang Deparmen of Economics,

More information

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1 Absrac number: 05-0407 Single-machine Scheduling wih Periodic Mainenance and boh Preempive and Non-preempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy

More information

Resiliency, the Neglected Dimension of Market Liquidity: Empirical Evidence from the New York Stock Exchange

Resiliency, the Neglected Dimension of Market Liquidity: Empirical Evidence from the New York Stock Exchange Resiliency, he Negleced Dimension of Marke Liquidiy: Empirical Evidence from he New York Sock Exchange Jiwei Dong 1 Lancaser Universiy, U.K. Alexander Kempf Universiä zu Köln, Germany Pradeep K. Yadav

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

News Intensity and Conditional Volatility on the US stock market

News Intensity and Conditional Volatility on the US stock market News Inensiy and Condiional Volailiy on he US sock marke Jean-Gabriel Cousin a, Tanguy de Launois b* a ESA, Universié de Lille II, France b FNRS Fellow a he Universié caholique de Louvain, Belgium ABSTRACT

More information

Trend-Cycle Interactions and the Subprime Crisis: Analysis of US and Canadian Output

Trend-Cycle Interactions and the Subprime Crisis: Analysis of US and Canadian Output Regensburger DISKUSSIONSBEITRÄGE zur Wirschafswissenschaf Universiy of Regensburg Working Papers in Business, Economics and Managemen Informaion Sysems Trend-Cycle Ineracions and he Subprime Crisis: Analysis

More information

Time-Expanded Sampling (TES) For Ensemble-based Data Assimilation Applied To Conventional And Satellite Observations

Time-Expanded Sampling (TES) For Ensemble-based Data Assimilation Applied To Conventional And Satellite Observations 27 h WAF/23 rd NWP, 29 June 3 July 2015, Chicago IL. 1 Time-Expanded Sampling (TES) For Ensemble-based Daa Assimilaion Applied To Convenional And Saellie Observaions Allen Zhao 1, Qin Xu 2, Yi Jin 1, Jusin

More information