time series 02
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逢甲大學財務金融系主任逢甲大學財務金融系主任張倉耀 教授張倉耀 教授
Applied EconometricTime-Series Data Analysis
Types of DataTypes of 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.
Time series dataTime series data1
Cross-sectional dataCross-sectional data2
Panel dataPanel data3
The Procedure to AnalysisThe Procedure to Analysis
Summary Statistics of DataSummary Statistics of DataSummary Statistics of DataSummary Statistics of Data
Linear ModelLinear ModelLinear ModelLinear Model Nonlinear ModelNonlinear ModelNonlinear ModelNonlinear Model
Luukkonen et al. (1988) Linearity TestLuukkonen et al. (1988) Linearity Test If rejectIf reject
not rejectnot reject
Basic Basic EconometricEconometric
Advanced Advanced EconometricEconometric
Economic or Financial TheoryEconomic or Financial TheoryEconomic or Financial TheoryEconomic or Financial Theory
DF-GLS, NP
KPSS
Time Series DataTime Series DataTime Series DataTime Series Data
Unit Root TestUnit Root TestUnit Root TestUnit Root Test
Phillips-Perron
Augmented DF
Dickey-Fuller
H0: Yt ~ I(1)H1: Yt ~ I(0)
H0: Yt ~ I(0)H1: Yt ~ I(1)
Non-StationarityNon-Stationarity StaionarutyStaionaruty
VAR in VAR in LevelLevel
Orders of IntegrationOrders of Integration
The Procedure to AnalysisThe Procedure to Analysis
DifferenceDifference
ARDL ARDL Bounding Bounding
TestTest
E-GE-GJ-JJ-J
H-I KPSS H-I KPSS
The sameThe same
Cointegration TestCointegration Test
Model SpecificationModel SpecificationModel SpecificationModel Specification
The Procedure to AnalysisThe Procedure to Analysis
Cointegration TestCointegration TestCointegration TestCointegration Test
NoNo
VAR in VAR in differdiffer
YesYes
UECMUECM(Pesaran (Pesaran
et al., et al., 2001)2001)
VECM VECM
Unit Root TestUnit Root TestUnit Root TestUnit Root Test
StaionarutyStaionaruty
VAR in VAR in LevelLevel
EG,JJ, KPSSEG,JJ, KPSS ARDLARDL
Economic or Finance Economic or Finance ImplicationImplication
Model EstimationModel EstimationModel EstimationModel Estimation
Impulse Impulse RespResp
Variance Variance DecDec
GrangerGrangerCausalityCausality
The Procedure to AnalysisThe Procedure to Analysis
The Procedure to AnalysisThe Procedure to Analysis
Diagnostic Diagnostic CheckingChecking
Goodness-of-fitGoodness-of-fit
R square
Error specificationError specification
Ramsey’s RESET
sationaritysationarity
CUSUM (square)
Series autocorrelationSeries autocorrelation
Ljung-Box Q, Q2
HeteroskedasticHeteroskedastic
ACH-LM Teat
NormalityNormality
Jarque-Bera N
Econometric Soft PackagesEconometric Soft Packages
PackagePackage
EViewsEViews
RatsRats
GAUSSGAUSS
MatlabMatlab
MicrofitMicrofit
EasyRegEasyReg
STATASTATA
TSPTSP
Sources of DataSources of Data
DataBaseDataBase WebsiteWebsite
AREMOSAREMOS http://140.111.1.22/moecc/rs/pkg/tedc/tedc1.htm
TEJ Data bank TEJ Data bank http://www.tej.com.tw/
National Statistic, National Statistic, ROCROC
http://www.stat.gov.tw/mp.asp?mp=4
DataStreamDataStream Thomson Financial DataStream
CRSPCRSP http://www.crsp.chicagogsb.edu/
CompustatCompustathttp://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 Frequency Sources
Currency exchange rate ls=Log (S)
Annual
(1979-1990)Hayashi (2000)
Price index of UK lukwpi=log (ukwpi)
Price index of US luswpi=log (uswpi)
Real exchange rate
tttt lukwpiluswpilse
Summary Statistics of DataSummary Statistics of Data
NNo trendo trend
Summary Statistics of DataSummary 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)
Moving Average, MA (1)
1 tttu
ttt uyy 10 ),0(~ 2WNut
Stationary Time Series
Box-Jenkins (1976) ARMA (p, q) model
The necessary and sufficient stationarity condition
qtqttptptt uuuyyy 11110
11
p
ii
q
iii
p
iiti uy
01
10
Stationary Time Series
The determination of the order of an ARMA process Autocorrelation function (ACF)
Partial ACF (PACF)
Ljung-Box Q statistic
)var(
),cov()(
t
qpttor y
yyqp or
2
1
2
~-
2)()( p
p
i
i
iTTTpQ
3,)(1
)()( 1
1 ,2,2
1
1 ,2,2
pp p
j jjppppjp
p
j jpjppppjpp
Stationary Time Series
processprocess ACF PACF
AR (p) Infinite: damps outFinite: cuts off after lag
p
MA (q)Finite: cuts off after lag
qInfinite: damps out
ARMA(p, q) Infinite: damps out Infinite: damps out
Stationary Time Series
PP* = 1* = 1
ee series is AR(1) series is AR(1)
Non-stationary Time Series
Autoregressive integrated moving average (ARIMA) model If
If
11
p
ii Y series is explosive
11
p
ii Y series has a unit root
Non-stationary Time Series
How to achieve stationary? DSP = Difference stationary process
• Yt ~ I(1) =
• Yt ~ I(2) =
TSP = Trend stationary process
ttttd yyyyD
11
ttttd yyyyD 2
12
tt ty 10 ty
Non-stationary Time Series
Unit Root Test ADF Test
KPSS
tit
p
iitt YYY
11:
tit
p
iittu YYY
11:
tit
p
iittt YYtY
11:
DDe-datae-data
DDe-trende-trend
DDe-meane-mean
),0(~ 2 NrtY
iid
tttt
Non-stationary Time Series
Selection Criteria of the Lag Length Schwartz Bayesian Criterion (SBC)
Akaike Information Criterion (AIC)
kT
SSRTAIC 2)ln(min
kT
T
Tk
T
SSRSBC
ln)ln( min
SSR sum of squared residuals
observations parameters
SSmall samplemall sample
Big Big samplesample
Non-stationary Time Series
RReject H0eject H0
Non-stationary Time Series
Engle-Granger 2-Stage Cointegration Test Step 1: regress real exchange rate
Step 2: error term
Hypothesis
ttttt ulukwpiluswpilse 3210
ttt uu 1
0:
0:
1
0
H
H)0(~ IutIf reject H0,
We support PPPWe support PPP
ADF Unit Root TestADF Unit Root Test
Non-stationary Time Series
NName as pppame as ppp
Non-stationary Time Series
Error – Correction Model (ECM)
Where x is independent variables
Residual ( ) Diagnostic Test
t
d
iit
d
iittt xeecme
1110
t
Non-stationary Time Series
逢甲大學財務金融系主任逢甲大學財務金融系主任張倉耀 教授張倉耀 教授
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