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
3
Cross-sectional data
Panel data
The Procedure to Analysis
Economic or Financial Theory
Summary Statistics of Data
If reject
not reject
Luukkonen et al. (1988) Linearity Test
Linear Model
Nonlinear Model
Basic
Econometric
Advanced
Econometric
The Procedure to Analysis
Time Series Data
Unit Root Test
Non-Stationarity
Staionaruty
Dickey-Fuller
Orders of Integration
Augmented DF
The same
Difference
Phillips-Perron
E-G
J-J
H-I KPSS
DF-GLS, NP
ARDL
Bounding
KPSS
Test
H0: Yt ~ I(1)
H1: Yt ~ I(0)
VAR in
Level
H0: Yt ~ I(0)
H1: Yt ~ I(1)
Cointegration Test
The Procedure to Analysis
Unit Root Test
Staionaruty
Cointegration Test
Yes
EG,JJ, KPSS
VECM
No
ARDL
UECM
(Pesaran
et al.,
2001)
VAR in
differ
Model Specification
VAR in
Level
The Procedure to Analysis
Model Estimation
Economic or Finance
Implication
Impulse
Resp
Variance
Dec
Granger
Causality
The Procedure to Analysis
Goodness-of-fit
Heteroskedastic
R square
ACH-LM Teat
Diagnostic
Checking
Normality
Jarque-Bera N
Series autocorrelation
Ljung-Box Q,
Error specification
Ramsey’s RESET
sationarity
Q2
CUSUM (square)
Econometric Soft Packages
Package
EViews
Rats
GAUSS
Matlab
Microfit
EasyReg
STATA
TSP
Sources of Data
DataBase
AREMOS
TEJ Data bank
National Statistic,
ROC
Website
http://140.111.1.22/moecc/rs/pkg/tedc/tedc1.htm
http://www.tej.com.tw/
http://www.stat.gov.tw/mp.asp?mp=4
DataStream
Thomson Financial DataStream
CRSP
http://www.crsp.chicagogsb.edu/
Compustat
http://www2.standardandpoors.com/portal/site/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
Currency exchange rate
Frequency
Sources
Annual
(1979-1990)
Hayashi
(2000)
ls=Log (S)
Price index of UK
lukwpi=log (ukwpi)
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
i 1
i 0
  0   i yt i   i u1i
 The necessary and sufficient stationarity condition
p

i 1
i
1
Stationary Time Series
 The determination of the order of an ARMA process
 Autocorrelation function (ACF)
cov( yt , yt  porq )
 ( por q) 
var( yt )
 Partial ACF (PACF)
 p   j 1 ( p  2, j   pp p  2, p  j )  p  j
p 1
 ( p) 
1   j 1 ( p  2, j   pp p  2, p  j )  j
p 1
 Ljung-Box Q statistic
p
i2
i 1
T -i
Q( p)  T (T  2)
~  p2
, p3
Stationary Time Series
process
ACF
PACF
AR (p)
Infinite: damps out
Finite: cuts off after lag
p
MA (q)
Finite: cuts off after lag
q
Infinite: damps out
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
i
1
Y series has a unit root
 If
p

i 1
Non-stationary Time Series
 How to achieve stationary?
 DSP = Difference stationary process
• Yt ~ I(1) = D
d 1
yt  yt  yt 1  yt
• Yt ~ I(2) =D d  2 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
i 1
De-data
p
 t : Yt     t  Yt 1    i Yt i   t
i 1
De-trend
p
 u : Yt    Yt 1    i Yt i   t
i 1
 KPSS
Yt  t  rt   t
iid
 t ~ N (0, 2 )
De-mean
Non-stationary Time Series
 Selection Criteria of the Lag Length
 Schwartz Bayesian Criterion (SBC)
SSR k ln T
min SBC  ln(
)
T
T
Small sample
 Akaike Information Criterion (AIC)
SSR
min AIC  T ln(
)  2k
T
k
T
SSR
Big sample
parameters
observations
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
i 1
i 1
et   0   ecmt 1   et i   xt i  t
 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