# Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014 MODELS

Save this PDF as:

Size: px
Start display at page:

Download "Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014 MODELS"

## Transcription

2 lem, resuls, analysis of he resuls and conclusion. 2. Univariae Models 2 Mehodology The Univariae approach in he presen paper is based on SARIMA models, which are a naural exension o he classical ARIMA models, which is a produc of wo ARIMA polynomials, one wih he regular srucure of he ime series, and he oher one wih he seasonal srucure of he ime series, as can be seen in (Box and Jenkins, 976; Hamilon,994 and Morein and Tolói, 2004). 2.2 Mulivariae Models The Mulivariae Models are mainly based on Vecor Auoregression models. These are nohing more han a mulivariable exension of he classical scalar auo regression models (AR), in he sense ha he process is described in erms of marices and vecors, insead of scalars. Thus, here is a muual causaliy relaionship beween all variables in his dynamic sysem. For example, a VAR(p) process can be wrien as: = φ +φ φ p p + a () where he φ i erms are square marices of order n ; n are x n vecors of endogenous variables; a is a x n vecor of uncorrelaed residuals; n is he endogenous variable number and p is he number of lags. In addiion o ha, as he classical scalar auo regression models (AR), if all variables are saionary, his model can be esimaed using he Ordinary Leas Squares (OLS) mehod. On he oher hand, when one or more variables in VAR models are non-saionary, he OLS resuls may be no valid anymore. Consequenly, he Theory of Coinegraion was developed in order o analyze hese possible relaionships beween non-saionary ime series. Furhermore, Granger and Newbold (974) discussed and exposed he problems of spurious regressions over non-saionary ime series. They also verified ha given wo series compleely uncorrelaed and non-saionary, he regression beween hem may produce a significan apparen relaionship. Therefore, if wo variables are non-saionary and have a long-run equilibrium relaionship, hey may be coinegraed ha is, boh are uncorrelaed, nonsaionary, bu wih a relaionship beween hem as exposed by Ashley and Granger (979), Engle and Granger (987) and Johansen (988). Thus Vecor Error Correcion Models (VEC) were developed, which can be seen as exensions o VAR according o Hendry and Juselius (2000, 200) and Lükepohl (99), where i is inroduced an error correcion erm. In order o verify he coinegraion assumpion, in he curren paper he approach ha was made is he verificaion ha all variables are non-saionary, using he Augmened Dickey-Fuller (979) es, using a 95 confidence inerval; hen if and only if he variables are non-saionary following Engle and Granger (987), he coinegraion residuals are obained by running a regression over he variables and hese residuals are esed for saionariy. If hese residuals are saionary (esed using he Augmened Dickey-Fuller es again) he ime series are coinegraed, oherwise hey are no coinegraed. In order o explain how he VEC model srucure is obained, one can sar from a wo variable dynamic sysem, where boh are coinegraed (by hypohesis), following (Hendry and Juselius, 2000, 200; Lükepohl, 99, 2004 and Morein, 20). Be, and 2, wo non-saionary coinegraed variables, and assume ha here is an equilibrium relaion beween hem given by:, β 2, = µ ~ N(0,σ ) (2) If considered ha he variaions in, and 2, depend on he deviaions of his equilibrium in -, i follows ha: Δ, = α (, β 2, )+ a, : a, ~ N(0,σ ) (3.) Δ 2, = α 2 (, β 2, )+ a 2, : a 2, ~ N(0,σ 2 ) (3.2) One can generalize his error correcion model ino a more general form, where hese correcions in he equilibrium may depend on previous changes in he equilibrium due o possible auocorrelaions, like: Δ, = α (, β 2, )+φ, Δ, +φ,2 Δ 2, + a, : a, ~ N(0,σ ) (4.) Δ 2, = α 2 (, β 2, )+φ 2, Δ, +φ 2,2 Δ 2, + a 2, : a 2, ~ N(0,σ 2 ) (4.2) where his model acually is a VAR() model. In order o verify ha, one can simply pu hese pair of equaions ino marix form, resuling in (5) and (6). where: Δ = αβ ' + AΔ + a (5) 626

3 α = α \$ α 2, β ' = β \$, A = φ, φ \$,2 φ 2, φ 2,2 or rewriing as: = ( αβ ' + A + I) A 2 + a (7) (6) Acually, according o Gujarai e al. (20) such relaionship can be generalized and guaraneed by he Granger Represenaion Theorem, which shows ha any VAR(p) can be wrien as a VEC(q) and viceversa. Depending on he auocorrelaion srucure, one migh find ineresing having a VEC(q) model and is respecive VAR(p). More deails can be found in (Greene, 2005). 3 Presenaion of he Problem In his paper, i is considered a VAR and a VEC model wih he following variables: raffic and Gross Domesic Produc () all of hem endogenous, and wo kinds of univariae SARIMA models, one wih a seasonal difference plus an sochasic seasonal shock, and anoher one wih an auoregressive seasonal erm. The is available a IPEA ( Insiuo de Pesquisas Econômicas Aplicadas Brazilian Insiue of Applied Economic Research) sie, while he oher series are publicly available upon reques o ARTESP Transporaion Regulaory Agency of São Paulo Sae, Brazil ( Agência Reguladora de Transpores do Esado de São Paulo ). The ime series encompasses monhly observaions from March 3 s, 998 unil July 3 s, 203. The las six observaions are lef o es he prevision accuracy of he model. In addiion o ha, i is possible o poin ou as a main concern he fac ha considering he Gross Domesic Produc as an endogenous variable may be couner-inuiive. However, i is known ha raffic can ac as a leading indicaor for he behavior, and acually, such assumpion is esed in his paper, hrough he verificaion of coinegraion beween boh variables. The raffic was normalized under an equivalen vehicle basis, in order o ransform differen ypes of vehicles in cars, e.g. a heavy ruck is equivalen o n cars, while a ligh ruck is equivalen o n-2 cars. The Seasonaliy in he vecor models was considered by including a vecor of dummy variables, since he daa is on a monhly basis. Then, having all he ime series normalized, considered he seasonal effecs, he rank of coinegraion and he number of lags mus be esablished. In his case, he rank of coinegraion is he number of coinegraing vecors which is esed according o (Johansen, 988) and he leas Informaion Crierion number deermines he number of lags, in boh univariae and mulivariae models, as suggesed in (Lükepohl and Kräzig, 2004). For mulivariae models, Bayesian Informaion Crierion was chosen, due o he fac ha i imposes sronger penalies for he inclusion of new parameers, as his kind of model naurally happens o have a larger number of parameers. On he oher hand, for univariae models, Akaike Informaion Crierion was used, due o he fac ha hese models generally have less parameers han he mulivariae ones. The esimaion of he parameers and all ess menioned are compued using GRETL Gnu Regression, Economerics and Time Library (for mulivariae models) and R (univariae models). 4 Resuls In Table, are presened he resuls of he Bayesian Informaion Crieria lag-search for mulivariae models. Table. Bayesian Informaion Crierion of he Lag Search. lags BIC * So, as can be seen in his able, he mulivariae models mus have only one lag. For he univariae models, i was esed down for he mos common lag composiions over shocks and auoregressive erms, according o he auo.arima funcion, provided in forecas package, wihin he R saisical sofware, o check he opimal ARIMA regular srucure. I resuled in an ARIMA polynomial of he form ARIMA (p=, d=, q=4). In words, a firs-order auo-regressive par; a firs-order difference over he original series; and four lags over he innovaions (shocks). Then, he wo mos usual seasonal polynomials were calibraed, SARIMA (p=, d=0, q=0) and SARIMA (p=0, d=, q=), following he same noaion above. The Rank of coinegraion was deermined according o he Johansen es (988), and for a null rank marix (null hypohesis), here is a p-value of So, he saisical evidence poins ou ha here is no coinegraing relaionship beween he variables. De- 627

4 spie ha, in his paper he VEC model was sill esimaed for comparison purposes. Thus, 4 differen models were obained as follows. Seasonal Model wih Seasonal Difference: Thus, if he monh o be prediced is January, one mus sum up he coefficien S plus he consan, and so on according o he respecive prediced monh. Finally, he VEC model wih seasonal dummies is presened as follows. Δ Δ a a a = Δ a a (8) Δ\$ ' = \$ + \$ ' \$ ' ' \$ [ ] + K \$ K 2 () ' ' Seasonal Model wih Auoregressive Seasonal componens: Δ = 0,5280 Δ a a Δ a a 2 VAR Model wih Seasonal Dummies: (0) \$ = \$ \$ + K \$ K 2 (9) where K and K are he seasonal dummies, as follows in Table 2 2. Table 2. Seasonal Parameers Esimaes of he VAR Model. K K2 S S S S S S S S S S S Consan where K and K are he seasonal dummies, as follows in Table 2 3: Table 3. Seasonal Parameer Esimaes of he VEC Model. K K2 S S S S S S S S S S S Consan Analysis of he Resuls Aiming he selecion of he bes model, he ou-ofsample forecasing accuracy is measured in erms of he absolue error mean, as follows. Table 4. Ou-of-sample Errors of he Models. Model ARIMA(,,4) - Seasonal IMA() ARIMA(,,4) - Seasonal AR() VAR() VEC() Mean Absolue Error Thus, he very surprising resul is ha he VEC() model, ha shouldn be even esimaed according o he exising lieraure, is he bes model in erms of ou-of-sample performance, despie he fac ha only six samples ou of he validaion se were used due o sampling issues, which may influence hese resuls. Noneheless, i was already expeced ha a mulivar- 628

5 Anais do XX Congresso Brasileiro de Auomáica iae model should perform beer han an univariae model, due o he fac ha more informaion is being included. Anoher ineresing fac is ha he loglikelihood of he univariae models are far worse han he mulivariae ones, as can be seen in Table 5 he model which has he larges log-likelihood is he bes one. he oher hand, vecor based models (Figure ) rely on seasonal deerminisic dummy variables. Thus, despie pas values are unknown o he auoregressive par, here are already values being insered in he model, providing esimaes of he seasonal flucuaions. Anoher ineresing poin is he fac ha, despie having a larger number of variables (mulivariae), hey had a poorer performance wihin he sample, so basically, he models which were acually overfied were he univariae ones. Finally, here i is shown he mos imporan feaure of vecor models in erms of policy analysis, which is he impulse response srucure ha can be rerieved of he sysem, following (Sims, 980). This mehod is based on he decomposiion of he covariance marix using a Cholesky algorihm, o obain wha is called a Srucural VAR/VEC. Table 5. Log-Likelihood of he Models. Model ARIMA(,,4) - Seasonal IMA() ARIMA(,,4) - Seasonal AR() VAR() VEC() Log- Likelihood Hence, based on hese resuls, i seems ha he backesing procedure is a very imporan par of he modeling process, since he log-likelihood esimae does no provide all necessary informaion o analyze which model is he bes. When analyzing he models fied values agains he observed values ( Obs in Figures and 2), i is possible o see ha SARIMA (Figure 2) models converge slower owards o he observed values han he vecor based models. I can be explained due he fac ha hese univariae seasonal models rely on pas observed values o forecas he seasonal facors. On Considering i as a VAR wih conemporaneous relaionships, as in he following expression. φ0 = φ + φ φn n + K + a (2) Muliplying he whole equaion by he inverse of φ0 one ges a VAR as in Equaion (), ha can be esimaed using he radiional OLS algorihm. 629

6 Anais do XX Congresso Brasileiro de Auomáica Therefore, afer decomposing he covariance marix, i is possible o impose causal resricions, in order o rerieve he conemporary relaionship marix. So, for example, if hough ha he economy () is expeced o cause he raffic in he road, one may infer how he dynamics beween he ime series may behave wih an impulse-response of he raffic agains he. This is a powerful ool ha enables he researcher o verify dynamic effecs insead of jus applying a firs-order (linear), as in he radiional simple linear regression over he logarihms of he variables (his procedure is acually called elasiciy calculaion ). 6 Conclusion In his paper i was shown ha i is possible o build an auoregressive mulivariable model o describe he raffic daa in one of he mos imporan Toll Road in Brazil, wih significan seasonal effecs and a large amoun of vehicles. Then, four kinds of models were esimaed: a VAR, a VEC and wo kinds of Seasonal ARIMA models. Furhermore, i were discussed mehodologies for esing he coinegraion beween he variables, uniary roo and opimal lag srucure obenion. Thus, i is possible o observe ha boh mulivariae mehodologies produced very similar forecass beween hem, as occurred beween boh univariae models oo. Despie ha, boh kinds of models were significanly differen in he long-run and in he shor-run, being he firs kind (mulivariae) he bes of hem, producing reasonable forecass 3 mean absolue error. Noneheless, i is imporan o noice ha his paper shows he usefulness of impulse-response analysis, which seems o be far more reasonable han he radiional elasiciy measures applied over simple linear regression based models in policy analysis. As perspecive for fuure analysis and work, i is suggesed expanding his analysis o oher large road sysems in Brazil and oher counries, coninuing o updae he exising daabase and verifying possible srucural and parameer changes in hese models, and include in his comparison he performance of NARX models (nonlinear auoregressive models) and sandard neural-nework based models, using only auoregressive componens of he dependen variable, or evaluae he inclusion of oher possible Figure 3. Impulse-Response of Trafego o a Shock in. As can be seen in Figure 3, a sandard shock (a uniary shock in erms of he covariance marix rerieved in he VAR/VEC models) in he evoluion of he causes an increase of 50 housand vehicles, afer 4 monhs and reaches sabiliy afer 5 monhs. 630

7 candidae independen variables (e.g. ). 7 References ASHLE, R.A., GRANGER, C.W.J. (979). Time series analysis of residuals from S. Louis model. In Journal of Macroeconomics,, BAIN, R. (2009). Error and opimism bias in oll road raffic forecass, Working Paper, RePEC. BOLSHINSKI, E., FREIDMAN, R. (202). Traffic flow forecas survey. Tech. rep., Technion Israel Insiue of Technology. BOX, G.E.P., JENKINS, G.M. (976). Times Series Analysis: Forecasing and Conrol. s Ediion, San Francisco Holden Day. DICKE, D.A., FULLER, W.A. (979) Disribuion of he esimaors for auoregressive ime seires wih a uni roo. In European Journal of Finance, vol. 5, p ENGLE, R.F., GRANGER, C.W.J. (987). Coinegraion and error correcion: Represenaion, esimaion and esing. In Economerica, vol. 55, FILLATRE, L., MARAKOV, D., VATON, S. December (2005). Forecasing Seasonal Traffic Flows. Workshop EuroNGI, Paris. GRANGER, C.W.J., NEWBOLD, P. (974). Spurious Regressions in Economerics, Journal of Economerics, vol. 2, -20. GREENE, W.H. (2002). Economeric Analysis, 5 h Ediion, Upper Saddle River, New Jersey, Prenice Hall. GUJARATI, D.N., PORTER, D.C. (20) Economeria Básica, Ediora Bookman, São Paulo. HAMILTON, J.D. (994). Time Series Analysis, s Ediion, Princeon, New Jersey, Princeon Universiy Press. HENDR, D.F., JUSELIUS, K. (2000). Explaining Coinegraion Analysis: Par. In The Energy Journal, Inernaional Associaion for Energy Economics, vol. 0 (Number ), -42 HENDR, D.F., JUSELIUS, K. (200). Explaining Coinegraion Analysis: Par 2. Em The Energy Journal, Inernaional Associaion for Energy Economics, vol. 0 (Number ), IPEADATA, no síio hp://www.ipeadaa.gov.br, visiado em 0//203. JOHANSEN, S. (988). Saisical Analysis of coinegraion vecors. In Journal of Economic Dynamics and Conrol, vol. 2, LÜTKEPOHL, H. (2004). Applied Time Series Economerics, s Ediion, New ork, Cambridge Universiy Press. LÜTKEPOHL, H. (99). Inroducion o Muliple Time Series Analysis, Heidelberg, Springer Verlag. MORETTIN, P.A. (20). Economeria Financeira: Um Curso em Séries Temporais Financeiras, ª Edição, São Paulo, Ediora Edgar Blücher. MORETTIN, P.A., TOLÓI, C. (2004). Análise de Séries Temporais, ª Edição, São Paulo, Ediora Edgar Blücher. SCHWARZ, G. (978). Esimaing he dimension of a model. In The Annals of Saisics, vol. 6, SIMS, C. (980). Macroeconomics and Realiy. In Economerica, vol. 48, no.,

### 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

### 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

### Cointegration Analysis of Exchange Rate in Foreign Exchange Market

Coinegraion Analysis of Exchange Rae in Foreign Exchange Marke Wang Jian, Wang Shu-li School of Economics, Wuhan Universiy of Technology, P.R.China, 430074 Absrac: This paper educed ha he series of exchange

### An empirical analysis about forecasting Tmall air-conditioning sales using time series model Yan Xia

An empirical analysis abou forecasing Tmall air-condiioning sales using ime series model Yan Xia Deparmen of Mahemaics, Ocean Universiy of China, China Absrac Time series model is a hospo in he research

### 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

### 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

### Impact of Debt on Primary Deficit and GSDP Gap in Odisha: Empirical Evidences

S.R. No. 002 10/2015/CEFT Impac of Deb on Primary Defici and GSDP Gap in Odisha: Empirical Evidences 1. Inroducion The excessive pressure of public expendiure over is revenue receip is financed hrough

### 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

### 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

### 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

### 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.

### 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

### 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,

### 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,

### Modelling and Forecasting Volatility of Gold Price with Other Precious Metals Prices by Univariate GARCH Models

Deparmen of Saisics Maser's Thesis Modelling and Forecasing Volailiy of Gold Price wih Oher Precious Meals Prices by Univariae GARCH Models Yuchen Du 1 Supervisor: Lars Forsberg 1 Yuchen.Du.84@suden.uu.se

### 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

### 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

### INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS

INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,

### 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

### 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

### Economics 140A Hypothesis Testing in Regression Models

Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1

### 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

### 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?

### 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

### 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,

### 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

### 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

### 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,

### 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

### Stock Price Prediction Using the ARIMA Model

2014 UKSim-AMSS 16h Inernaional Conference on Compuer Modelling and Simulaion Sock Price Predicion Using he ARIMA Model 1 Ayodele A. Adebiyi., 2 Aderemi O. Adewumi 1,2 School of Mahemaic, Saisics & Compuer

### 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

### 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

### A New Type of Combination Forecasting Method Based on PLS

American Journal of Operaions Research, 2012, 2, 408-416 hp://dx.doi.org/10.4236/ajor.2012.23049 Published Online Sepember 2012 (hp://www.scirp.org/journal/ajor) A New Type of Combinaion Forecasing Mehod

### Distributing Human Resources among Software Development Projects 1

Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources

### 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

### Title: Who Influences Latin American Stock Market Returns? China versus USA

Cenre for Global Finance Working Paper Series (ISSN 2041-1596) Paper Number: 05/10 Tile: Who Influences Lain American Sock Marke Reurns? China versus USA Auhor(s): J.G. Garza-García; M.E. Vera-Juárez Cenre

### Abstract: Key Words: Documentos Técnico-Científicos

Documenos Técnico-Cieníficos Commom Economic Cycles in Brazil s Norheas Marcos Cosa Holanda Professor Tiular do Deparameno de Economia Aplicada e do Curso de Mesrado em Economia da Universidade Federal

### ECONOMETRIC MODELLING AND FORECASTING OF FREIGHT TRANSPORT DEMAND IN GREAT BRITAIN

ECONOMETRIC MODELLING AND FORECASTING OF FREIGHT TRANSPORT DEMAND IN GREAT BRITAIN Shujie Shen, Tony Fowkes, Tony Whieing and Daniel Johnson Insiue for Transpor Sudies, Universiy of Leeds, Leeds, UK, LS2

### 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

### 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

### 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,

### 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

### Improvement in Forecasting Accuracy Using the Hybrid Model of ARFIMA and Feed Forward Neural Network

American Journal of Inelligen Sysems 2012, 2(2): 12-17 DOI: 10.5923/j.ajis.20120202.02 Improvemen in Forecasing Accuracy Using he Hybrid Model of ARFIMA and Feed Forward Neural Nework Cagdas Hakan Aladag

### Hedging with Forwards and Futures

Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buy-side of a forward/fuures

### 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

### A DCC Analysis of Two Stock Market Returns Volatility with an Oil Price Factor: An Evidence Study of Singapore and Thailand s Stock Markets

Journal of Convergence Informaion Technology Volume 4, Number 1, March 9 A DCC Analysis of Two Sock Marke Reurns Volailiy wih an Oil Price Facor: An Evidence Sudy of Singapore and Thailand s Sock Markes

### 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

### 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

### 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

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

### Chapter 4. Properties of the Least Squares Estimators. Assumptions of the Simple Linear Regression Model. SR3. var(e t ) = σ 2 = var(y t )

Chaper 4 Properies of he Leas Squares Esimaors Assumpions of he Simple Linear Regression Model SR1. SR. y = β 1 + β x + e E(e ) = 0 E[y ] = β 1 + β x SR3. var(e ) = σ = var(y ) SR4. cov(e i, e j ) = cov(y

### 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

### 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

### 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

### Trend and Cycle in the Euro-Area: A Permanent-Transitory Decomposition Using a Cointegrated VAR Model

Viereljahrshefe zur Wirschafsforschung 7. Jahrgang, Hef 3/2 S. 352 363 Trend and Cycle in he Euro-Area: A Permanen-Transiory Decomposiion Using a Coinegraed VAR Model By Chrisian Schumacher* Summary This

### Purchasing Power Parity (PPP), Sweden before and after EURO times

School of Economics and Managemen Purchasing Power Pariy (PPP), Sweden before and afer EURO imes - Uni Roo Tes - Coinegraion Tes Masers hesis in Saisics - Spring 2008 Auhors: Mansoor, Rashid Smora, Ami

### 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

### 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

### Graphing the Von Bertalanffy Growth Equation

file: d:\b173-2013\von_beralanffy.wpd dae: Sepember 23, 2013 Inroducion Graphing he Von Beralanffy Growh Equaion Previously, we calculaed regressions of TL on SL for fish size daa and ploed he daa and

### Demand and Price Forecasting Models for Strategic and Planning Decisions in a Supply Chain

Proc. Schl. ITE Tokai Univ. vol.3,no,,pp.37-4 Vol.,No.,,pp. - Paper Demand and Price Forecasing Models for Sraegic and Planning Decisions in a Supply Chain by Vichuda WATTANARAT *, Phounsakda PHIMPHAVONG

### Modeling Tourist Arrivals Using Time Series Analysis: Evidence From Australia

Journal of Mahemaics and Saisics 8 (3): 348-360, 2012 ISSN 1549-3644 2012 Science Publicaions Modeling Touris Arrivals Using Time Series Analysis: Evidence From Ausralia 1 Gurudeo AnandTularam, 2 Vicor

### 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

### Forecasting Sales: A Model and Some Evidence from the Retail Industry. Russell Lundholm Sarah McVay Taylor Randall

Forecasing Sales: A odel and Some Evidence from he eail Indusry ussell Lundholm Sarah cvay aylor andall Why forecas financial saemens? Seems obvious, bu wo common criicisms: Who cares, can we can look

### 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

### A Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)

A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke

### Do Property-Casualty Insurance Underwriting Margins Have Unit Roots?

Do Propery-Casualy Insurance Underwriing Margins Have Uni Roos? Sco E. Harringon* Moore School of Business Universiy of Souh Carolina Columbia, SC 98 harringon@moore.sc.edu (83) 777-495 Tong Yu College

### Chapter 1 Overview of Time Series

Chaper 1 Overview of Time Series 1.1 Inroducion 1 1.2 Analysis Mehods and SAS/ETS Sofware 2 1.2.1 Opions 2 1.2.2 How SAS/ETS Sofware Procedures Inerrelae 4 1.3 Simple Models: Regression 6 1.3.1 Linear

### Supply chain management of consumer goods based on linear forecasting models

Supply chain managemen of consumer goods based on linear forecasing models Parícia Ramos (paricia.ramos@inescporo.p) INESC TEC, ISCAP, Insiuo Poliécnico do Poro Rua Dr. Robero Frias, 378 4200-465, Poro,

### 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

### Time Series Analysis using In a Nutshell

1 Time Series Analysis using In a Nushell dr. JJM J.J.M. Rijpkema Eindhoven Universiy of Technology, dep. Mahemaics & Compuer Science P.O.Box 513, 5600 MB Eindhoven, NL 2012 j.j.m.rijpkema@ue.nl Sochasic

### PARAMETRIC EXTREME VAR WITH LONG-RUN VOLATILITY: COMPARING OIL AND GAS COMPANIES OF BRAZIL AND USA.

Perspecivas Globais para a Engenharia de Produção Foraleza, CE, Brasil, 13 a 16 de ouubro de 015. PARAMETRIC EXTREME VAR WITH LONG-RUN VOLATILITY: COMPARING OIL AND GAS COMPANIES OF BRAZIL AND USA. RICARDO

### An integrated econometric + input-output model for the Brazilian economy: an application to the energy sector 1 ABSTRACT

An inegraed economeric + inpu-oupu model for he Brazilian economy: an applicaion o he energy secor 1 ABSTRACT Fernando Salgueiro Perobelli Rogério Silva de Maos Eduardo Amaral Haddad Marcos Paulo Novaes

### Representing Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1

Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals

### Determinants of Capital Structure: Comparison of Empirical Evidence from the Use of Different Estimators

Serrasqueiro and Nunes, Inernaional Journal of Applied Economics, 5(1), 14-29 14 Deerminans of Capial Srucure: Comparison of Empirical Evidence from he Use of Differen Esimaors Zélia Serrasqueiro * and

### 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

### Chabot College Physics Lab RC Circuits Scott Hildreth

Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard

### Dynamic Hedge Rations on Currency Futures. Bartosz Czekierda and Wei Zhang

Dynamic Hedge Raions on Currency Fuures Barosz Czekierda and Wei Zhang Graduae School Maser of Science in Finance Maser Degree Projec No.2010:135 Supervisor: Charles Nadeau and Joakim Weserlund Absrac

### How much depreciation of the US dollar for sustainability of the current accounts?

How much depreciaion of he US dollar for susainabiliy of he curren accouns? Eiji Ogawa and Taeshi Kudo Firs version: May 27, 2004 This version: June 6, 2004 This paper is prepared for a conference of he

### 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

### Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand

Forecasing and Informaion Sharing in Supply Chains Under Quasi-ARMA Demand Avi Giloni, Clifford Hurvich, Sridhar Seshadri July 9, 2009 Absrac In his paper, we revisi he problem of demand propagaion in

### The Impact of Flood Damages on Production of Iran s Agricultural Sector

Middle-Eas Journal of Scienific Research 12 (7): 921-926, 2012 ISSN 1990-9233 IDOSI Publicaions, 2012 DOI: 10.5829/idosi.mejsr.2012.12.7.1783 The Impac of Flood Damages on Producion of Iran s Agriculural

### 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

### Hotel Room Demand Forecasting via Observed Reservation Information

Proceedings of he Asia Pacific Indusrial Engineering & Managemen Sysems Conference 0 V. Kachivichyanuul, H.T. Luong, and R. Piaaso Eds. Hoel Room Demand Forecasing via Observed Reservaion Informaion aragain

### 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

### Task is a schedulable entity, i.e., a thread

Real-Time Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T: - s: saring poin - e: processing ime of T - d: deadline of T - p: period of T Periodic ask T

### 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

### 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

### Chapter 4: Exponential and Logarithmic Functions

Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion

### Causal Relationship between Macro-Economic Indicators and Stock Market in India

Asian Journal of Finance & Accouning Causal Relaionship beween Macro-Economic Indicaors and Sock Marke in India Dr. Naliniprava ripahy Associae Professor (Finance), Indian Insiue of Managemen Shillong

### A comparison of the Lee-Carter model and AR-ARCH model for forecasting mortality rates

A comparison of he Lee-Carer model and AR-ARCH model for forecasing moraliy raes Rosella Giacomei a, Marida Berocchi b, Svelozar T. Rachev c, Frank J. Fabozzi d,e a Rosella Giacomei Deparmen of Mahemaics,

### 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:

### Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17

### Constant Data Length Retrieval for Video Servers with Variable Bit Rate Streams

IEEE Inernaional Conference on Mulimedia Compuing & Sysems, June 17-3, 1996, in Hiroshima, Japan, p. 151-155 Consan Lengh Rerieval for Video Servers wih Variable Bi Rae Sreams Erns Biersack, Frédéric Thiesse,

### Applied Econometrics and International Development

Applied Economerics and Inernaional Developmen Vol.6-3(006) STANDARD & POOR S DEPOSITARY RECEIPTS AND THE MARKET QUALITY OF S&P 500 INDEX FUTURES CHU, Quenin C. * KAYALI, Musafa Mesu Absrac This sudy examines

### FORECASTING WATER DEMAND FOR AGRICULTURAL, INDUSTRIAL AND DOMESTIC USE IN LIBYA

Inernaional Review of Business Research Papers Vol.4 No. 5 Ocober-November 8 Pp. 31-48 FORECASTING WATER DEMAND FOR AGRICULTURAL, INDUSTRIAL AND DOMESTIC USE IN LIBYA Fahis F. Lawgali* This paper examines

### 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

### The Kinetics of the Stock Markets

Asia Pacific Managemen Review (00) 7(1), 1-4 The Kineics of he Sock Markes Hsinan Hsu * and Bin-Juin Lin ** (received July 001; revision received Ocober 001;acceped November 001) This paper applies he

### Optimal Longevity Hedging Strategy for Insurance. Companies Considering Basis Risk. Draft Submission to Longevity 10 Conference

Opimal Longeviy Hedging Sraegy for Insurance Companies Considering Basis Risk Draf Submission o Longeviy 10 Conference Sharon S. Yang Professor, Deparmen of Finance, Naional Cenral Universiy, Taiwan. E-mail: