Time Series Analysis Using SAS R Part I The Augmented DickeyFuller (ADF) Test


 Sydney Cook
 2 years ago
 Views:
Transcription
1 ABSTRACT Time Series Analysis Using SAS R Par I The Augmened DickeyFuller (ADF) Tes By Ismail E. Mohamed The purpose of his series of aricles is o discuss SAS programming echniques specifically designed o simulae he seps involved in ime series daa analysis. The firs par of his series will cover he Augmened DickeyFuller (ADF) es of ime series (saionariy es). The second par will cover coinegraion and error correcion. The SAS echniques presened in boh pars can be used wih he more complex SAS rouines such as PROC ARIMA, which require a high level of research and analysis experise (Bails & Peppers, 1982). INTRODUCTION Time series daa analysis has many applicaions in many areas including sudying he relaionship beween wages and house prices, profis and dividends, and consumpion and GDP. Many analyss erroneously use he framework of linear regression (OLS) models o predic change over ime or exrapolae from presen condiions o fuure condiions. Exreme cauion is needed when inerpreing he resuls of regression models esimaed using ime series daa. Saisicians and analyss working wih ime series daa uncovered a serious problem wih sandard analysis echniques applied o ime series. Esimaion of parameers of he Ordinary Leas Square Regression (OLS) model produced saisically significan resuls beween ime series ha conain a rend and are oherwise random. This finding led o considerable work on how o deermine wha properies a ime series mus possess if economeric echniques are o be used. One basic conclusion was ha any imes series used in economeric applicaions mus be saionary (Granger and Newbold, 1974). This paper will discuss a simple SAS framework o assis SAS programmers in undersanding and modeling ime series daa as a univariae series (Eq 1). Y = α + β X + ε (1) BASICS AND TERMINOLOGY Time series daases are differen from oher ordinary daases in ha heir observaions are recorded sequenially over equal ime incremens (daily, weekly, monhly, quarerly, annually ec). A simple example of a ime series daase (RawDaa) is illusraed below. YEAR QTR X Y Each of x and y is called a series, while he combinaion of he 2 variables YEAR and QTR represen he sequenial equal ime incremens. If x and y series are boh nonsaionary random processes (inegraed), hen modeling he x, y relaionship as a simple OLS relaionship as in equaion 1 will only generae a spurious regression. Granger and Newbold (1974) inroduced he noion of a spurious regression which hey argued produces saisically significan resuls beween series ha conain a rend and are oherwise random. Time series saionariy is a saisical characerisic of a series mean and variance over ime. If boh are consan over ime, hen he series is said o be a saionary process (i.e. is no a random walk/has 1
2 no uni roo), oherwise, he series is described as being a nonsaionary process (i.e. a random walk/has uni roo). Differencing echniques are normally used o ransform a ime series from a nonsaionary o saionary by subracing each daum in a series from is predecessor. As such, he se of observaions ha correspond o he iniial ime period () when he measuremen was aken describes he series level. Differencing a series using differencing operaions produces oher ses of observaions such as he firsdifferenced values, he seconddifferenced values and so on. x level x x 1 s differenced value x  x 1 x 2 nd differenced value x  x 2 If a series is saionary wihou any differencing i is designaed as I(0), or inegraed of order 0. On he oher hand, a series ha has saionary firs differences is designaed I(1), or inegraed of order 1. Saionariy of a series is an imporan phenomenon because i can influence is behavior. For example, he erm shock is used frequenly o indicae an unexpeced change in he value of a variable (or error). For a saionary series a shock will gradually die away. Tha is, he effec of a shock during ime will have a smaller effec in ime +1, a sill smaller effec in ime +2, ec. The daa used in his paper assumed o represens ime series daa. Each series in equaion 1 namely, x and y requires examinaions a level for saionariy before proceeding furher o invesigae he relaionship beween he wo variables (he OLS regression analysis). In his specificaion, because he daa used by he paper is a quarerly series, saionariy esing will be conduced a level for up o 5lagged periods. The saionariy es will uilize he Augmened DickeyFuller (ADF) echnique (Dickey and Fuller (1981) which is a generalized auoregression model formulaed in he following regression equaion (Dickey and Fuller (1981) 5 x = κ x + ϖ xi, + ε i, i, 1 i, k k k, k = 1 The model hypoheses of ineres are: The Series is (2) H O: Nonsaionary H A: Saionary ADF Saisics is compared o Criical values o draw conclusions abou Saionariy (see Dickey and Fuller, 1979 for he criical values) AN ANATOMY OF AN ADF EQUATION x i, = κx i, 1 + k 5 = 1 ϖ, k + ε k, i xi +, k This is he 1sdifferenced value of x This is he 1slagged value of x These are he 1s, 2nd, 3rd, 4h, & 5hlagged of 1sdifferenced of values of x This is he error erm The above elemens can be easily seen in he following char. 2
3 SAS TECHNIQUES As i was menioned earlier ha our sample daa is quarerly spaced, his dicaes ha five lagged differences have o be included in esing of saionariy of boh series (x and y) for more explanaory power. The following SAS Daa sep creaes he firs lagged, he firs differenced and he five laggeddifferenced values of he x series. A similar sep is needed o creae he same variables from he y series. The SAS Daa sep explois he power of SAS LAG and DIF funcions o creae he se of he lagged and differenced values of x. SAS LAG funcion simply looks back in he daase nh number of records and allows you o obain a previous value of a variable and sore i in he curren observaion. 'n' refers o he number of records back in he daa and can be an ineger from 1 o 99. Many imes he only hing you wan o do wih a previous value of a variable is o compare i wih he curren value o compue he difference. I is always recommended ha he LAG and DIF funcions no o be execued condiionally because hey could cause unexpeced resuls. If you have o use hem wih condiional processing of a daase, firs execue he funcions and assign heir resuls o a new variable, hen use he new variable for he condiional processing. The DIF n funcion works he same way as LAG n, bu raher han simply assigning a value, i assigns he difference beween he curren value and a previous value of a variable. The saemen A = DIF n ( X ) ells SAS ha A should equal he curren value of x minus he value x had nh number of records back in he ime. Boh LAG and DIF funcions should only be used on he righ hand side of assignmen saemens and again should no be execued condiionally. DATA TimeSeries; SET RawDaa; RUN; x_1 s _LAG = LAG1(x); x_1 s _DIFF = DIF1(x); x_1 s _DIFF_1 s _LAG = DIF1(LAG1(x)); x_1 s _DIFF_2 nd _LAG = DIF1(LAG2(x)); x_1 s _DIFF_3 rd _LAG = DIF1(LAG3(x)); x_1 s _DIFF_4 h _LAG = DIF1(LAG4(x)); x_1 s _DIFF_5 h _LAG = DIF1(LAG5(x)); SAS Oupu (parial): 1 s _lagged, 1 s _differenced, and he 1 s 5 h _lagged values of he 1 s _differenced value of x DIFF_ DIFF_ DIFF_ DIFF_ DIFF_ YEAR QTR X LAG DIFF 1 _LAG 2 _LAG 3 _LAG 4 _LAG 5 _LAG Nex he SAS REG procedure, one of many regression procedures in he SAS Sysem is used in he analysis o regress he lagged and differenced values of x generaed by he above daa sep. The regression model used here was se as a relaionship in which he value of x a he preceding ime period (lagged value 3
4 of x) is he dependen variable and he independen variables are he se of 5 previousdifferenced values of he x series. This analysis provides a "besfi" mahemaical equaion for he relaionship exhibied in Eq (2). SAS REG procedure for Uni Roo Tes a level, wih fixed 5 Lag Lengh and a Consan : PROC REG DATA = TimeSeries; MODEL x_1s_diff = x_1s_lag x_1s _DIFF_1s _LAG x_1s _DIFF_2nd_LAG x_1s _DIFF_3rd_LAG x_1s _DIFF_4h_LAG x_1s _DIFF_5h_LAG; RUN; QUIT; DISCUSSION The x_1 s _LAG value generaed by he above regression model corresponds o he Augmened Dickey Fuller es (ADF) Saisics. Compare his value o he Criical Values (see Dickey and Fuller, 1979 for he criical values) o es he hypoheses ha he x series is: H O: NonSaionary H A: Saionary In our example he value of (1.83) is greaer han he Criical Values (CVs) a 1%, 5%, and 10% significan level ( , , and respecively). We would fail o rejec he null hypohesis and conclude ha he x series is a nonsaionary process when esed a level. WHAT IS NEXT? If we fail o rejec he null hypohesis, and concluded ha x and perhaps y are nonsaionary series, we would have o difference each series once, creae a se of lagged and differenced variables as shown in he earlier SAS daa sep his ime from he differencedvalues of each series, and finally carry ou he ADF es (esing he series saionariy a is firsdifferenced value). Differencing of a series normally ransforms i from nonsaionariy o saionariy. A differenced saionary series is said o be inegraed and is denoed as I(d) where d is he order of inegraion. The order of inegraion is he number of uni roos conained in he series, or he number of differencing operaions i akes o make he series saionary. For our purpose here, since we will difference our example series once, here is one uni roo, so i is an I(1) series. Once boh x and y deermined nonsaionary a heir level, we will move furher o examine he naure of heir linear combinaion. Specifically we will be ineresed in examining he linear combinaion beween he nonsaionary x and y, if such a linear combinaion exiss, hen x and y series are said o be coinegraed. The linear combinaion beween hem is he coinegraing equaion and may be inerpreed as he longrun equilibrium relaionship among he 2 variables. Forunaely, his es can also be accomplished using he Augmened DickeyFuller es and will be he subjec of discussion of he second par of his series of aricles. 4
5 SAS Oupu Regression Analysis (Uni Roo Tes) Level wih 5 Lags NULL HYPOTHESIS: 'x' has a uni roo LAG LENGTH: 5 (FIXED) AUGMENTED DICKEYFULLER TEST STATISTICS, TEST CRITICAL VALUES: 1% LEVEL TSTATISTICS = % LEVEL TSTATISTICS = % LEVEL TSTATISTICS = LEVEL WITH 5 LAGS The REG Procedure Model: MODEL1 Dependen Variable: x_1 s _DIFF Number of Observaions Read 78 Number of Observaions Used 72 Number of Observaions wih Missing Values 6 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model <.0001 Error Correced Toal Roo MSE RSquare Dependen Mean Adj RSq Coeff Var Parameer Esimaes The hypohesis ha x has a uni roo canno be rejeced Parameer Sandard Variable DF Esimae Error Value Pr > Inercep x_1 s _LAG x_1 s _DIFF_1 s _LAG x_1 s _DIFF_2 nd _LAG x_1 s _DIFF_3 rd _LAG x_1 s _DIFF_4 h _LAG x_1 s _DIFF_5 h _LAG EVIEWS R1 CODE AND OUTPUT FOR COMPARISON Similarly, EVIEWS or oher SAS ime series ools can be used o carry ou he same es. The following EVIEWS Code can be used o carry ou he ADF es. Resuls of his code are shown in he nex page. Uroo(adf,cons,lag=5,save=mou) 1 EVIEWS is an economerics & Time Series Analysis sofware package by Quaniaive Micro Sofware. hp:// 5
6 The hypohesis ha x has a uni roo canno be rejeced REFERENCES Bails, Dale G. and Larry C. Peppers (1982) Business Flucuaions: Forecasing Techniques and Applicaions, Englewood Cliffs NJ: PreniceHall Inc. Dickey, D. and W. Fuller (1979). Disribuion of he Esimaors for Auoregressive Time Series wih a Uni Roo, Journal of he American Saisical Associaion, 74, Fuller, W. (1996). Inroducion o Saisical Time Series, Second Ediion. John Wiley, New York. Granger, C.W.J., and P. Newbold(1974). Spurious regressions in economerics, Journal of Economerics, 2, Hamilon (1994). Time Series Analysis, Princeon Universiy Press. Phillips, P.C.B. (1987). Time Series Regression wih a Uni Roo, Economerica, 55, ACKNOWLEDGEMENTS My sincere hanks o everyone I have had he pleasure of exchanging ime Series analysis relaed ideas wih in recen years. Special hanks o Theresa Diveni, Ian Keih boh wih he Financial Insiuions Regulaion Division, Kee N. Cheung wih he Housing Finance Analysis Division of he U.S. Deparmen of Housing and Urban Developmen, and Ronald Hanson wih L3 Communicaions, Enerprise IT Soluions (EITS), for heir consrucive suggesions which added much o his paper. TRADEMARKS SAS and all oher SAS Insiue Inc. produc or service names are regisered rademarks or rademarks of SAS Insiue Inc. in he USA and oher counries. EVIEWS and all oher EVIEWS produc or service names are regisered rademarks or rademarks of Quaniaive Micro Sofware in he USA and oher counries. Indicaes USA regisraion. The auhor welcomes and encourages any quesions, correcions, improvemens, feedback, remarks, boh on and offopic via . Please conac he auhor: Ismail E. Mohamed, Ph.D Sofware Engineer 5, L3 Communicaions, Enerprise IT Soluions (EITS), U.S. Deparmen of Housing & Urban Developmen, 451 7h Sree, SW, Room 8212, Washingon, DC 20410; Phone:
Cointegration: The Engle and Granger approach
Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be nonsaionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require
More informationChapter 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 informationCointegration Analysis of Exchange Rate in Foreign Exchange Market
Coinegraion Analysis of Exchange Rae in Foreign Exchange Marke Wang Jian, Wang Shuli School of Economics, Wuhan Universiy of Technology, P.R.China, 430074 Absrac: This paper educed ha he series of exchange
More informationUsefulness 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 informationEconomics 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
More informationINVESTIGATION 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,
More informationJournal 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 YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationAn empirical analysis about forecasting Tmall airconditioning sales using time series model Yan Xia
An empirical analysis abou forecasing Tmall aircondiioning 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
More informationTEMPORAL 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 informationForecasting Malaysian Gold Using. GARCH Model
Applied Mahemaical Sciences, Vol. 7, 2013, no. 58, 28792884 HIKARI Ld, www.mhikari.com Forecasing Malaysian Gold Using GARCH Model Pung Yean Ping 1, Nor Hamizah Miswan 2 and Maizah Hura Ahmad 3 Deparmen
More informationCAUSAL 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 informationMultiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States
Deparmen of Economics Discussion Paper 0007 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 informationMeasuring macroeconomic volatility Applications to export revenue data, 19702005
FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a
More informationWhy 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 informationThe 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 imeseries smoohing forecasing mehods. Various models are discussed,
More informationPurchasing 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
More informationChapter 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
More informationIssues 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 informationThe 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 informationRESTRICTIONS IN REGRESSION MODEL
RESTRICTIONS IN REGRESSION MODEL Seema Jaggi and N. Sivaramane IASRI, Library Avenue, New Delhi11001 seema@iasri.res.in; sivaramane@iasri.res.in Regression analysis is used o esablish a relaionship via
More informationPrice 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 informationFourier Series Solution of the Heat Equation
Fourier Series Soluion of he Hea Equaion Physical Applicaion; he Hea Equaion In he early nineeenh cenury Joseph Fourier, a French scienis and mahemaician who had accompanied Napoleon on his Egypian campaign,
More informationDo PropertyCasualty Insurance Underwriting Margins Have Unit Roots?
Do ProperyCasualy 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) 777495 Tong Yu College
More informationThe Kinetics of the Stock Markets
Asia Pacific Managemen Review (00) 7(1), 14 The Kineics of he Sock Markes Hsinan Hsu * and BinJuin Lin ** (received July 001; revision received Ocober 001;acceped November 001) This paper applies he
More informationDYNAMIC 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 informationThe Relationship Between Consumer Sentiment and Stock Prices
The Relaionship Beween Consumer Senimen and Sock Prices by Kevin P. Chris Assisan Professor of Economics, RoseHulman Insiue of Technology and Dale S. Bremmer Professor of Economics, RoseHulman Insiue
More informationImpact 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
More informationUSE 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 informationResearch Question Is the average body temperature of healthy adults 98.6 F? Introduction to Hypothesis Testing. Statistical Hypothesis
Inroducion o Hypohesis Tesing Research Quesion Is he average body emperaure of healhy aduls 98.6 F? HT  1 HT  2 Scienific Mehod 1. Sae research hypoheses or quesions. µ = 98.6? 2. Gaher daa or evidence
More informationVector 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), 101115. Macroeconomericians
More informationChapter 8 Student Lecture Notes 81
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 informationLead 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 SNFprojec No. 7220: Gassmarkeder, menneskelig kapial og selskapssraegier The projec is financed
More informationCausal Relationship between MacroEconomic Indicators and Stock Market in India
Asian Journal of Finance & Accouning Causal Relaionship beween MacroEconomic Indicaors and Sock Marke in India Dr. Naliniprava ripahy Associae Professor (Finance), Indian Insiue of Managemen Shillong
More informationPart 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 informationThe Relationship Between Commercial Energy Consumption and Gross Domestic Income in Kenya
The Relaionship Beween Commercial Energy Consumpion and Gross Domesic Income in Kenya Susan M. Onuonga The Journal of Developing Areas, Volume 46, Number 1, Spring 2012, pp. 305314 (Aricle) Published
More informationHouse 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 informationStock Price Prediction Using the ARIMA Model
2014 UKSimAMSS 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
More informationDistributing 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
More informationTime Series Modeling for Risk of Stock. Price with Value at Risk Computation
Applied Mahemaical Sciences, Vol 9, 015, no 56, 779787 HIKARI Ld, wwwmhikaricom hp://dxdoiorg/101988/ams0155144 Time Series Modeling for Risk of Sock Price wih Value a Risk Compuaion Dodi Deviano, Maiyasri
More informationStochastic 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 informationTitle: Who Influences Latin American Stock Market Returns? China versus USA
Cenre for Global Finance Working Paper Series (ISSN 20411596) Paper Number: 05/10 Tile: Who Influences Lain American Sock Marke Reurns? China versus USA Auhor(s): J.G. GarzaGarcía; M.E. VeraJuárez Cenre
More informationGraphing the Von Bertalanffy Growth Equation
file: d:\b1732013\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
More informationA PROPOSAL TO OBTAIN A LONG QUARTERLY CHILEAN GDP SERIES *
CUADERNOS DE ECONOMÍA, VOL. 43 (NOVIEMBRE), PP. 285299, 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 informationINTRODUCTION 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 informationRelative velocity in one dimension
Connexions module: m13618 1 Relaive velociy in one dimension Sunil Kumar Singh This work is produced by The Connexions Projec and licensed under he Creaive Commons Aribuion License Absrac All quaniies
More informationCapacitors and inductors
Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear
More informationA Reexamination of the Joint Mortality Functions
Norh merican cuarial Journal Volume 6, Number 1, p.166170 (2002) Reeaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali
More informationWorking Paper A fractionally integrated exponential model for UK unemployment
econsor www.econsor.eu Der OpenAccessPublikaionsserver der ZBW LeibnizInformaionszenrum Wirschaf The Open Access Publicaion Server of he ZBW Leibniz Informaion Cenre for Economics GilAlaña, Luis A.
More informationThe 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 informationDOES 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 informationTHE 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 informationMALAYSIAN FOREIGN DIRECT INVESTMENT AND GROWTH: DOES STABILITY MATTER? Jarita Duasa 1
Journal of Economic Cooperaion, 8, (007), 8398 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 information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS 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 cuingedge
More informationDIFFERENTIAL EQUATIONS with TI89 ABDUL HASSEN and JAY SCHIFFMAN. A. Direction Fields and Graphs of Differential Equations
DIFFERENTIAL EQUATIONS wih TI89 ABDUL HASSEN and JAY SCHIFFMAN We will assume ha he reader is familiar wih he calculaor s keyboard and he basic operaions. In paricular we have assumed ha he reader knows
More informationOil 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 AbdulRahman,
More informationThe 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 informationDeterminants of Capital Structure: Comparison of Empirical Evidence from the Use of Different Estimators
Serrasqueiro and Nunes, Inernaional Journal of Applied Economics, 5(1), 1429 14 Deerminans of Capial Srucure: Comparison of Empirical Evidence from he Use of Differen Esimaors Zélia Serrasqueiro * and
More informationEfficiency in Emerging Markets  Evidence from the Emirates Securities Market
European Journal of Economics, Finance and Adminisraive Sciences ISSN 4502275 Issue 2 (2008) EuroJournals, Inc. 2008 hp://www.eurojournalsn.com Efficiency in Emerging Mares  Evidence from he Emiraes
More informationDuration 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 UVAF38 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 informationMultiprocessor SystemsonChips
Par of: Muliprocessor SysemsonChips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,
More informationElectricityConsumptionandEconomicGrowthinBangladeshCoIntegrationandCausalityAnalysis
Global Journal of Managemen and Business Research Volume 12 Issue 11 Version 1.0 July 2012 Type: Double Blind Peer Reviewed Inernaional Research Journal Publisher: Global Journals Inc. (US) Online ISSN:
More informationFakultet for informasjonsteknologi, Institutt for matematiske fag
Page 1 of 5 NTNU Noregs eknisknaurviskaplege universie Fakule for informasjonseknologi, maemaikk og elekroeknikk Insiu for maemaiske fag  English Conac during exam: John Tyssedal 73593534/41645376 Exam
More informationThe Relation between Price Changes and Trading Volume: A Study in Indian Stock Market
Inerdisciplinary Journal of esearch in Business ol. 1, Issue. 7, July 011(pp.8195) The elaion beween Price Changes and Trading olume: A Sudy in Indian Sock Marke Dr. Naliniprava Tripahy Associae Professor
More informationSPEC 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 informationHow 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
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationPrice and Income Elasticity of Australian Retail Finance: An Autoregressive Distributed Lag (ARDL) Approach
Ausralasian Accouning Business and Finance Journal Volume 8 Issue 1 Aricle 7 Price and Income Elasiciy of Ausralian Reail Finance: An Auoregressive Disribued Lag (ARDL) Approach Helen Higgs Griffih Universiy,
More informationDiane K. Michelson, SAS Institute Inc, Cary, NC Annie Dudley Zangi, SAS Institute Inc, Cary, NC
ABSTRACT Paper DK02 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 informationStability. Coefficients may change over time. Evolution of the economy Policy changes
Sabiliy Coefficiens may change over ime Evoluion of he economy Policy changes Time Varying Parameers y = α + x β + Coefficiens depend on he ime period If he coefficiens vary randomly and are unpredicable,
More informationANALYSIS 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 informationReporting to Management
CHAPTER 31 Reporing o Managemen Inroducion The success or oherwise of any business underaking depends primarily on earning revenue ha would generae sufficien resources for sound growh. To achieve his objecive,
More informationConsumer sentiment is arguably the
Does Consumer Senimen Predic Regional Consumpion? Thomas A. Garre, Rubén HernándezMurillo, and Michael T. Owyang This paper ess he abiliy of consumer senimen o predic reail spending a he sae level. The
More informationMathematics 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 informationA 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
More informationA 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
More informationRelationship between Stock Returns and Trading Volume: Domestic and CrossCountry Evidence in Asian Stock Markets
Proceedings of he 2013 Inernaional Conference on Economics and Business Adminisraion Relaionship beween Sock Reurns and Trading olume: Domesic and CrossCounry Evidence in Asian Sock Markes KiHong Choi
More informationARCH 2013.1 Proceedings
Aricle from: ARCH 213.1 Proceedings Augus 14, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationFORECASTING WATER DEMAND FOR AGRICULTURAL, INDUSTRIAL AND DOMESTIC USE IN LIBYA
Inernaional Review of Business Research Papers Vol.4 No. 5 OcoberNovember 8 Pp. 3148 FORECASTING WATER DEMAND FOR AGRICULTURAL, INDUSTRIAL AND DOMESTIC USE IN LIBYA Fahis F. Lawgali* This paper examines
More informationHANDOUT 14. A.) Introduction: Many actions in life are reversible. * Examples: Simple One: a closed door can be opened and an open door can be closed.
Inverse Funcions Reference Angles Inverse Trig Problems Trig Indeniies HANDOUT 4 INVERSE FUNCTIONS KEY POINTS A.) Inroducion: Many acions in life are reversible. * Examples: Simple One: a closed door can
More informationAnalogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar
Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 073807 Ifeachor
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationTerm 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 111 Nojihigashi, Kusasu, Shiga 5258577, Japan Email:
More informationGoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results:
For more informaion on geneics and on Rheumaoid Arhriis: Published work referred o in he resuls: The geneics revoluion and he assaul on rheumaoid arhriis. A review by Michael Seldin, Crisopher Amos, Ryk
More informationOptimal 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. Email:
More informationDoes Capital Punishment Have a Deterrence Effect on the Murder Rate? Issues and Evidence
Does Capal Punishmen Have a Deerrence Effec on he Murder Rae? Issues and Evidence Seven S. Cuellar, Ph.D.* Deparmen of Economics Sonoma Sae Universy 181 Eas Coai Avenue Rohner Park, CA 998 () 5 Seve.Cuellar@Sonoma.edu
More informationMeasuring the Downside Risk of the ExchangeTraded Funds: Do the Volatility Estimators Matter?
Proceedings of he Firs European Academic Research Conference on Global Business, Economics, Finance and Social Sciences (EAR5Ialy Conference) ISBN: 97863450286 MilanIaly, June 30July 2, 205, Paper
More informationChapter 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
More informationUnderstanding Sequential Circuit Timing
ENGIN112: Inroducion o Elecrical and Compuer Engineering Fall 2003 Prof. Russell Tessier Undersanding Sequenial Circui Timing Perhaps he wo mos disinguishing characerisics of a compuer are is processor
More informationModeling Tourist Arrivals Using Time Series Analysis: Evidence From Australia
Journal of Mahemaics and Saisics 8 (3): 348360, 2012 ISSN 15493644 2012 Science Publicaions Modeling Touris Arrivals Using Time Series Analysis: Evidence From Ausralia 1 Gurudeo AnandTularam, 2 Vicor
More informationHedging 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 buyside of a forward/fuures
More informationPremium 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 informationContrarian insider trading and earnings management around seasoned equity offerings; SEOs
Journal of Finance and Accounancy Conrarian insider rading and earnings managemen around seasoned equiy offerings; SEOs ABSTRACT Lorea Baryeh Towson Universiy This sudy aemps o resolve he differences in
More informationPayment Plans of Reverse Mortgage System in the Korean. Housing Market. Deokho Cho a, Seungryul Ma b,
1 Paymen Plans of Reverse Morgage Sysem in he Korean Housing Marke Deokho Cho a, Seungryul Ma b, a Deparmen of Public Adminisraion, Daegu Universiy, Gyeongbuk, Souh Korea b Deparmen of Insurance and Finance,
More informationANOMALIES IN INDIAN STOCK MARKET AN EMPIRICAL EVIDENCE FROM SEASONALITY EFFECT ON BSEIT INDEX
Journal of Ars, Science & Commerce ANOMALIES IN INDIAN STOCK MARKET AN EMPIRICAL EVIDENCE FROM SEASONALITY EFFECT ON BSEIT INDEX Dr. Pedapalli Neeraja, M.Com., M.Phil. Ph.D. Assisan Professor Business
More informationPerformance Center Overview. Performance Center Overview 1
Performance Cener Overview Performance Cener Overview 1 ODJFS Performance Cener ce Cener New Performance Cener Model Performance Cener Projec Meeings Performance Cener Execuive Meeings Performance Cener
More informationRepresenting 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
More informationPROFIT 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 informationInternational Business & Economics Research Journal March 2007 Volume 6, Number 3
Weak Form Efficiency In Indian Sock Markes Rakesh Gupa, (Email: r.gupa@cqu.edu.au), Cenral Queensland Universiy, Ausralia Parikshi K. Basu, (Email: pbasu@csu.edu.au), Charles Sur Universiy, Ausralia
More information