FINANCIAL TIME-SERIES ECONOMETRICSMar 2, 2002SUN LI JIAN

INTRODUCTION

Contents 1. Models,Data and ProcessThe nature of the econometric approachThe Process of an econometric analysis 2. Applications of Financial EconometricsDynamic effects of various shocksEmpirical financeRefining data 3. Key Features of Financial Time Series The regression modelTime series modelsDynamic model 4. Contents of Time Series ModelingStationary stochastic time series modelNonstationary stochastic processMultiple time series modeling

Time series models of heteroskedasticityState space model 5. Text and SoftwareTextSoftware 6. Some Basic ToolsDifference equations and their solutionsSolution methodologyStability conditionsImpulse response functionThe basics of time series analysis software 7. Summary and Conclusions Appendix: TSP Program to Accompany Chapter 1 Box: Empirical Research on Exchange Rate Bibliography

1. MODELS, DATA AND PROCESSThe Nature of The Econometric Approachstructural analysisevaluationforecastingThe Process of An Empirical Analysismodel specification structural equations and reduced formsparameters conditionssampling and refining dataIdentification and estimationstatistical testeconomic interpretation

Econometric Approach

Theory

Facts

Model

Data

Statistical Theory

Econometric Theory

Refined Data

Econometric Techniques

Estimation of Econometric Model with the Refined Data Using Econometric Techniques

Evaluation

Forecasting

Structural Analysis

Structural AnalysisEconometric ModelLinear model Greene (2000)Nonlinear model* Davidson Mackinnon (1993) Static modelTime series model Enders 1995Dynamic model Christian Gourieroux (1997)Structure Change Maddala and Kim,1998)Chow testTime-varying parameters

EvaluationThe Simulation ApproachIdentificationLimited-information estimationFull-information estimationMonte Carlo studies

Other ApproachesThe Instruments-targets approachThe Social-welfare-function approach

ForecastingForecasting MethodsSample informationEconomic theory

Introduction to Forecasting TechniquesTime series model (ARIMA,GARCH,KALMAN-filter)Statistical model (Monte Carlo techniques,MSFE)

Data and RefiningTypeQuantitative versus qualitative dataTime-series versus cross-section data (Panel Data)Non-experimental versus experimental data Micro versus macro dataNatureDegrees of freedomMulticollinearitySerial correlationStructural changeErrors in measurementNon-stationary SourceIMF international financial statistics (CD-ROM)

2. APPLICATIONS OF FINANCIAL ECONOMETRICSDynamic Effects of Various ShocksTransmission mechanism of financial crisisCredit channel of policyEmpirical FinanceForecasting(price of capital assets, risk premium,etc.) Predictability of asset returnsMarket microstructureTerm structureFinancial integrationRefining DataMissing dataBase changes (GDP,M1,etc.)Nonstationary (EX,IR,etc.)

3. KEY FEASURES OF FINANCIAL TIME SERIESThe Regression ModelThe Method of ordinary least squaresAssumption (disturbance term;observations, independent variables)The Gauss-Markov theorem (BLUE,consistency)Other methods of estimationMaximum likelihoodMomentsBayesian approachThe Probability distribution for OLS estimatorParameters and disturbance termt,F,P tests and significance (confidence intervals)Applications (structural break,prediction,model selection)ExtensionsDiagnosis and treatment

Time Series ModelsDifferences between LRM and TSM Exogenous variables,sequence,theoryComponentsTrendsSeasonalityCycleIrregularity (convergence)Conditional heteroskedasticity (volatility)Non-linearity (state dependency)DeterminantsFunction structure:Lag order: Dynamic ModelTransfer process (impulse response function)

4. CONTENTS OF TIME SERIES MODELINGStationary Stochastic Time Series ModelARMAARIMANonstationary Stochastic ProcessUnit root testCointegration and error correction modelMultiple Time Series ModelingVARGranger testStructural VARTime Series Models of HeteroskedasticityARCHGARCHState Space ModelKALMAN filterRegime switching model

Other Useful Financial Econometric ModelsMethods of Instrumental Variables GMMDiscrete and Limited Dependent Variable ModelsProbit,logit and tobit modelsComputationally Intensive MethodsMonte Carlo methodsThe bootstrapPermutation testNonparametric and semiparametric estimationPanel Data AnalysisSurvival Data AnalysisEvent-Study Analysis

5. TEXT AND SOFTWARETextEnders,Walter. (1995) Applied Econometric Time Series. John Wiley & Sons,Inc.TSP (Ver.4.4) Reference Manual (1997)Greene,William H. (2000) Econometrics Analysis.4th ed. Prentice-Hall International,Inc. Software (http://emlab.berkeley.edu)TSP,SHAZAM,RATSGAUSS,S-PLUSSPSS,SAS,STATAMathematica,Excel

6. SOME BASIC TOOLSDifference Equations and Their SolutionsThe special form of nth-order linear difference equation

The special form of the forcing process

The solution form of difference equations

Solution MethodologyIteration (e.g. first-order)With initial condition:forward from the specific periodWithout initial Condition: backward to infinity

Structural decomposition methods e.g. General solution:Homogeneous solution Characteristic equation and characteristic root

Particular solution (challenge solution) (1)Method of undetermined coefficients

(2)Lag operators for , then for , then

Stability ConditionsInside unit circleNecessary condition:

Sufficient condition:Unit root processUnit root exit, ifImpulse Response FunctionThe effect of stochastic shock:

The Basics of Time Series Analysis SoftwareStarting and quittingInteractive mode batch modeFundamental program structure and some important commandsConstructing and manipulating dataData set-up(frequency,numbers)Data input(external file;format;subsets)Data transformation(dynamic equation;order change)Refining data(seasonality,etc.)Descriptive statistics(mean,variance,correlation,etc.)Data output(print,plot,output,type,etc.)Linear regression analysisAnalysis command(OLS)The interpretation of the test statistics The economical implication of empirical results

7. SUMMARY AND CONCLUSIONSEconometrics utilizes economic theory,facts(data) and statistical techniques,to measure and to test certain relationships among economic variables,thereby giving these results to economic reasoning.Empirical finance provides analytical tools needed to examines the behavior of financial markets.Topics covered include estimating the dynamic impact multiplier of financial shocks,forecasting the value of capital assets,measuring the volatility of asset returns, testing the financial integration, and more.Time-series econometrics is concerned with the estimation of difference equations containing stochastic components. These solution can be divided into two parts: a homogeneous portion and particular portion .The former is especially important in that it yields the characteristic roots which determine the system stability,the latter will be solved by the use of lag operators.This chapter introduces some basic concepts of the soft used to time series analysis and describes commands for setting up observations, reading data,making transformation,and illustrating OLS estimation method.

Appendix : TSP Programs to Accompany IntroductionOPTIONS CRT;? Monetary Approach to Exchange RateFREQ M;SMPL 80 :1,90:12;LOAD(FILE=C:\DATA\EXCISE1.XLS);PRINT SJA MJA IJA YJA MGE IGE YGE;? Data statistic descriptionMSD(CORR,COVA)MJA MGE IJA IGE;? Data transformations SJAGE=SJA/SGE;LOGSJAGE=LOG(SJAGE);LOGM=LOG(MJA)-LOG(MGE);DI=IJA-IGE;LOGY=LOG(YJA)-LOG(YGE);PLOT LOGM * LOGY +;PLOT DI %;

? Empirical analysis (technique:OLS)OLSQ LOGSJAGE C LOGM DI LOGY;ESLSJAGE=@FIT;ESRES=@RES;PLOT LOGSJAGE + ESLSJAGE*;PLOT ESRES %;END;

Box: Empirical research on Exchange RateCASE OF MONETARIST APPROACHAssumption: (a) perfect substitutes in consumer demand functions (b) perfect substitutes between domestic and foreign bonds (c) domestic and foreign elasticities are equalModel: (1) (2) (3) (4) (5)

BibliographyCampell,J.Y., Lo,A.W. and MacKinlay,A.C. (1997) The Econometrics of Financial Markets. Princeton University Press.Frankel,J. A. and A.K.Rose (1995) Empirical research on nominal exchange rates. In G.M.Grossman and K.Rogoff,eds., Handbook of international economics, vol.3. Amsterdam:North Holland.Hodrick, R. (1978) An empirical analysis of the monetary approach to the determination of the exchange rate. In J.Frenkel and H.G.Johnson,eds., The Economics of Exchange Rates, Addison-Wesley.

Time-series analysis can be roughly divided into tow types of methods: frequency-domain methods and time-domain methods. The former methods is called spectral analysis.But it would be too difficult for beginner to understand.