Transcript FINANCIAL TIME-SERIES ECONOMETRICS

FINANCIAL TIME-SERIES
ECONOMETRICS
SUN LI JIAN
Mar 2, 2002
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
Theor
y
Facts
Model
Econometric Approach
Data
Econometri
c Theory
Refined
Data
Statistic
al
Theory
Econometri
c
Techniques
Estimation of Econometric Model with the
Refined Data Using Econometric
Techniques
Evaluatio
Time Series Analysis
n
Forecasting
Structural
Analysis
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( yt
   xt  ut )
– 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
• Time Series Models[ xt  f ( xt 1, xt 2 ,...xt  p , ut )]
– 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:f
• Lag order: p
• Dynamic Model [ yt  f ( xt , yt 1, yt 2 ,...yt  p , ut )]
– Transfer process (impulse response function)
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
Analysis.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
n

– The special
nth-order
equation
y form
 a of
a ylineardifference
u
t
0
i 1
i
t i
t

– The special form of
the forcing process
ut   i t i
i 0
t 1
t 1
i
– The solution
form
of
difference
equations
(
y

a
a

a
y

a
 1 t i )
yt  f  t , t, C 
t
0
0
i 0
i
1
t
1
i 0
• Solution Methodology
( y0 )
(i 
)
• With initial condition:forward from the specific
period
• Without initial Condition: backward to infinity
– Iteration (e.g. first-order)
– Structural decomposition methods
e.g. yt  a0  a1 yt 1  a2 yt 2 ut
h
dp
sp
y

y

y

y
General solution: t
t
t
t
(ut  utd  uts )
• Homogeneous solution
Characteristic equation and characteristic root
{d  [(a1 )2  4a2 ]}
d  0  yth  A t
d  0  yth  t t ; yth  A t
d  0  yth  1rt cos(t  2 )
r  (a2 )1/ 2 ; cos( )  a1 /[2(a2 )1/ 2 ]
• Particular solution (challenge solution)
(1)Method of undetermined coefficients
utd  0  ytdp  c

u   t  y  i t i
s
t
sp
t
i 0
(2)Lag operators( Li yt  yt i )
for a  1 , then
(1  aL  a2 L2  a3L3  ) yt  yt /(1  aL)
for a  1 , thenyt /(1  aL)  (aL)
1

 (aL)
i 0
• Stability Conditions
– Inside unit circle
n
• Necessary condition:  ai  1
i 1
n
a
• Sufficient condition:
– Unit root process
i 1
i
1
n
a  1
• Impulse Response Function
• Unit root exit, if
i 1
i
– The effect of stochastic shock:
pt 1n
 g (t , C )
 t
i
yt
• 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 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) mt  pt  yt  it   t (mt  pt  yt  it  t )

s

p

p
(2) t
t
t  t



s

(
m

m
)


(
y

y
)


(
i

i
)t  ut
(3) t
t
t

(4) (i  i )t  Et ( st 1  st )  t



s

(
m

m
)


(
y

y
)


E
(



)t 1   t
(5) t
t
t
t
Bibliography
• Campell,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, AddisonWesley.