Applied Econometric

Time-Series Data Analysis

逢甲大學財務金融系主任
張倉耀 教授
 Types of Data

1 Time series data

 Data have been collected over a period of
time on one or more variables.
 Data have associated with them a particular
frequency of observation (daily, monthly or
annually…) or collection of data points.

2 Cross-sectional data

3 Panel data
The Procedure to Analysis
Economic
Economic or
or Financial
Financial Theory
Theory

Summary
Summary Statistics
Statistics of
of Data
Data

Luukkonen et al. (1988) Linearity Test

not reject

If reject
Linear
Linear Model
Model Nonlinear
Nonlinear Model
Model
Basic Advanced
Econometric Econometric
 The Procedure to Analysis
Time
Time Series
Series Data
Data

Unit
Unit Root
Root Test
Test

Non-Stationarity Staionaruty
Dickey-Fuller

Augmented DF
Orders of Integration H0: Yt ~ I(1)
The same Difference H1: Yt ~ I(0)
Phillips-Perron
VAR in
E-G DF-GLS, NP
Level
J-J ARDL
Bounding H0: Yt ~ I(0)
H-I KPSS
KPSS
Test
H1: Yt ~ I(1)
Cointegration Test
The Procedure to Analysis

Unit
Unit Root
Root Test
Test
Staionaruty

Cointegration
Cointegration Test
Test
Yes No

EG,JJ, KPSS ARDL

UECM
(Pesaran
VECM et al., VAR in
VAR in
2001) Level
differ

Model
Model Specification
Specification
The Procedure to Analysis

Model
Model Estimation
Estimation

Economic or Finance
Implication

Impulse Variance Granger

Resp Dec Causality
 The Procedure to Analysis

Heteroskedastic Goodness-of-fit
ACH-LM Teat R square

Normality Diagnostic Error specification

Checking
Jarque-Bera N Ramsey’s RESET

Series autocorrelation
sationarity
Ljung-Box Q, Q2
CUSUM (square)
Econometric Soft Packages

Package
EViews

Rats

GAUSS

Matlab

Microfit

EasyReg

STATA

TSP
 Sources of Data

DataBase Website
AREMOS http://140.111.1.22/moecc/rs/pkg/tedc/tedc1.htm
TEJ Data bank http://www.tej.com.tw/
National Statistic,
http://www.stat.gov.tw/mp.asp?mp=4
ROC
DataStream Thomson Financial DataStream
CRSP http://www.crsp.chicagogsb.edu/
http://www2.standardandpoors.com/portal/site/
Compustat sp/en/us/page.product/dataservices_compustat/
2,9,2,0,0,0,0,0,0,0,0,0,0,0,0,0.html
 Example: PPP

Variables Frequency Sources

Currency exchange rate ls=Log (S)

Annual Hayashi
Price index of UK lukwpi=log (ukwpi)
(1979-1990) (2000)
Price index of US luswpi=log (uswpi)

 Real exchange rate

et  lst  luswpit  lukwpit

Summary Statistics of Data

No trend
Summary Statistics of Data
 Stationary Time Series
 Time Series modeling
 A series is modeled only in terms of its own past values
and some disturbance.

 Autoregressive, AR (1)
yt   0  1 yt  ut ut ~ WN (0, 2 )

 Moving Average, MA (1)

ut   t    t 1
 Stationary Time Series
 Box-Jenkins (1976) ARMA (p, q) model
yt   0  1 yt 1     p yt  p  ut  1ut 1     q ut  q
p q
  0    i yt i    i u1i
i 1 i 0

 The necessary and sufficient stationarity condition


i 1
i 1
 Stationary Time Series
 The determination of the order of an ARMA process
 Autocorrelation function (ACF)
cov( yt , yt  por q )
 ( por q) 
var( yt )

 Partial ACF (PACF)

 p   j 1 ( p  2, j   pp p  2, p  j )  p  j
p 1

 ( p)  , p3
1   j 1 ( p  2, j   pp p  2, p  j )  j
p 1

 Ljung-Box Q statistic
p
 i2
Q( p )  T (T  2) ~  p2
i 1 T -i
 Stationary Time Series

process ACF PACF

Finite: cuts off after lag

AR (p) Infinite: damps out
p
Finite: cuts off after lag
MA (q) Infinite: damps out
q
ARMA(p,
q)
Infinite: damps out Infinite: damps out
 Stationary Time Series

e series is AR(1)

P* = 1
 Non-stationary Time Series
 Autoregressive integrated moving average
(ARIMA) model
 If
p


i 1
i 1 Y series is explosive

 If
p


i 1
i 1 Y series has a unit root
 Non-stationary Time Series
 How to achieve stationary?
 DSP = Difference stationary process
d 1
• Yt ~ I(1) = D yt  yt  yt 1  yt
d 2
• Yt ~ I(2) =D yt  yt  yt 1  2 yt

 TSP = Trend stationary process

yt   0  1t  t ŷt
 Non-stationary Time Series
 Unit Root Test
 ADF Test
p
 : Yt  Yt 1    i Yt i   t De-data
i 1 p
 t : Yt     t  Yt 1    i Yt i   t De-trend
i 1
p
 u : Yt    Yt 1    i Yt i   t De-mean
i 1

 KPSS
iid
Yt  t  rt   t  t ~ N (0, 2 )
 Non-stationary Time Series
 Selection Criteria of the Lag Length
 Schwartz Bayesian Criterion (SBC)
SSR k ln T
min SBC  ln( ) Small sample
T T
 Akaike Information Criterion (AIC)
SSR
min AIC  T ln( )  2k Big sample
T

k parameters
T observations
SSR sum of squared residuals
Non-stationary Time Series

Reject H0
 Non-stationary Time Series

 Engle-Granger 2-Stage Cointegration Test

 Step 1: regress real exchange rate

et   0  1lst   2luswpit   3lukwpit  ut

 Step 2: error term

ut   ut 1   t ADF Unit Root Test

 Hypothesis
H0 :  0
H1 :   0
If reject H0, ut ~ I (0)
We support PPP
Non-stationary Time Series

Name as ppp
 Non-stationary Time Series
 Error – Correction Model (ECM)
d d
et   0   ecmt 1    et i    xt i  t
i 1 i 1

 Where x is independent variables

 Residual (  t ) Diagnostic Test

Non-stationary Time Series
逢甲大學財務金融系主任
張倉耀 教授