FINANCIAL TIME-SERIES ECONOMETRICS

FINANCIAL TIME-SERIES ECONOMETRICS

Mar 2, 2002Mar 2, 2002

SUN LI JIANSUN LI JIAN

INTRODUCTION

Contents 1. Models,Data and Process

– The nature of the econometric approach– The Process of an econometric analysis

2. Applications of Financial Econometrics– Dynamic effects of various shocks– Empirical finance– Refining data

3. Key Features of Financial Time Series – The regression model– Time series models– Dynamic model

4. Contents of Time Series Modeling– Stationary stochastic time series model– Nonstationary stochastic process– Multiple time series modeling

– Time series models of heteroskedasticity– State space model

5. Text and Software– Text– Software

6. Some Basic Tools– Difference equations and their solutions– Solution methodology– Stability conditions– Impulse response function– The 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 PROCESS

• The Nature of The Econometric Approach– structural analysis– evaluation– forecasting

• The Process of An Empirical Analysis– model specification

structural equations and reduced forms– parameters conditions– sampling and refining data– Identification and estimation– statistical test– economic interpretation

Time Series Analysis

Theory

Facts

Model DataStatistic

al Theory

Econometric Theory

Refined Data

Econometric

Techniques

Estimation of Econometric Model with the Refined Data Using Econometric

Techniques

Evaluation

Forecasting Structural Analysis

Econometric Approach Econometric Approach

Structural Analysis• Econometric Model

– Linear model Greene (2000)– Nonlinear model* Davidson Mackinnon (1993) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •– Static model– Time series model Enders （ 1995）– Dynamic model Christian Gourieroux (1997)

• Structure Change （Maddala and Kim,1998)

– Chow test– Time-varying parameters

Evaluation

• The Simulation Approach– Identification

– Limited-information estimation

– Full-information estimation

– Monte Carlo studies

• Other Approaches– The Instruments-targets approach

– The Social-welfare-function approach

Forecasting

• Forecasting Methods– Sample information

– Economic theory

• Introduction to Forecasting Techniques– Time series model (ARIMA,GARCH,KALMAN-filter)

– Statistical model (Monte Carlo techniques,MSFE)

Data and Refining• Type

– Quantitative versus qualitative data– Time-series versus cross-section data (Panel Data)– Non-experimental versus experimental data – Micro versus macro data

• Nature– Degrees of freedom– Multicollinearity– Serial correlation– Structural change– Errors in measurement– Non-stationary

• Source– IMF international financial statistics (CD-ROM)

2. APPLICATIONS OF FINANCIAL ECONOMETRICS

• Dynamic Effects of Various Shocks– Transmission mechanism of financial crisis– Credit channel of policy

• Empirical Finance– Forecasting(price of capital assets, risk premium,etc.) – Predictability of asset returns– Market microstructure– Term structure– Financial integration

• Refining Data– Missing data– Base changes (GDP,M1,etc.)– Nonstationary (EX,IR,etc.)

3. KEY FEASURES OF FINANCIAL TIME SERIES

• The Regression Model– The Method of ordinary least squares

• Assumption (disturbance term;observations, independent variables)

• The Gauss-Markov theorem (BLUE,consistency)– Other methods of estimation

• Maximum likelihood• Moments• Bayesian approach

– The Probability distribution for OLS estimator• Parameters and disturbance term• t,F,P tests and significance (confidence intervals)• Applications (structural break,prediction,model selection)

– Extensions• Diagnosis and treatment

)( ttt uxy

• Time Series Models– Differences between LRM and TSM

• Exogenous variables,sequence,theory

– Components• Trends• Seasonality• Cycle• Irregularity (convergence)• Conditional heteroskedasticity (volatility)• Non-linearity (state dependency)

– Determinants• Function structure:• Lag order:

• Dynamic Model– Transfer process (impulse response function)

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fp

)],,...,,([ 21 tpttttt uyyyxfy

4. CONTENTS OF TIME SERIES MODELING• Stationary Stochastic Time Series Model

– ARMA– ARIMA

• Nonstationary Stochastic Process– Unit root test– Cointegration and error correction model

• Multiple Time Series Modeling– VAR– Granger test– Structural VAR

• Time Series Models of Heteroskedasticity– ARCH– GARCH

• State Space Model– KALMAN filter– Regime switching model

Other Useful Financial Econometric Models

• Methods of Instrumental Variables • GMM• Discrete and Limited Dependent Variable Models

– Probit,logit and tobit models

• Computationally Intensive Methods– Monte Carlo methods– The bootstrap– Permutation test– Nonparametric and semiparametric estimation

• Panel Data Analysis• Survival Data Analysis• Event-Study Analysis

5. TEXT AND SOFTWARE• Text 

– Enders,Walter. (1995) Applied Econometric Time Series. John Wiley & Sons,Inc.

– TSP (Ver.4.4) Reference Manual (1997)– Greene,William H. (2000) Econometrics Analysi

s.4th ed. Prentice-Hall International,Inc.

• Software (http://emlab.berkeley.edu)– TSP,SHAZAM,RATS– GAUSS,S-PLUS– SPSS,SAS,STATA– Mathematica,Excel

6. SOME BASIC TOOLS• Difference Equations and Their Solutions

– The special form of nth-order linear difference equation

– The special form of the forcing process

– The solution form of difference equations

• Solution Methodology– Iteration (e.g. first-order)

• With initial condition:forward from the specific period• Without initial Condition: backward to infinity

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– Structural decomposition methods

e.g.

General solution:• Homogeneous solution

Characteristic equation and characteristic root

• Particular solution (challenge solution)

(1)Method of undetermined coefficients

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(2)Lag operators

for , then

for , then

• Stability Conditions– Inside unit circle

• Necessary condition:

• Sufficient condition:

– Unit root process• Unit root exit, if

• Impulse Response Function– The effect of stochastic shock:

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• The Basics of Time Series Analysis Software– Starting and quitting

• Interactive mode • batch mode• Fundamental program structure and some important commands

– Constructing and manipulating data• Data 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 analysis• Analysis command(OLS)• The interpretation of the test statistics • The economical implication of empirical results

7. SUMMARY AND CONCLUSIONS• Econometrics 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 Introduction

OPTIONS CRT;

? Monetary Approach to Exchange Rate

FREQ M;

SMPL 80 :1,90:12;

LOAD(FILE=‘C:\DATA\EXCISE1.XLS);

PRINT SJA MJA IJA YJA MGE IGE YGE;

? Data statistic description

MSD(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 Rate

CASE OF MONETARIST APPROACHCASE OF MONETARIST APPROACH– Assumption: (a) perfect substitutes in consumer demand functions

(b) perfect substitutes between domestic and foreign bonds

(c) domestic and foreign elasticities are equal

– Model:

(1)

(2)

(3)

(4)

(5)

ttttt iypm tttt pps

ttttt uiiyymms )()()( ttttt ssEii

)()( 1

tttttt Eyymms

1)()()(

)( ttttt iypm

Bibliography• Campell,J.Y., Lo,A.W. and MacKinlay,A.C. (1997) The Econometrics o

f 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.