time series 02

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


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


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



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


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


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


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


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


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


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


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


RReject H0eject H0


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


NName as pppame as ppp


Error – Correction Model (ECM)

Where x is independent variables

Residual ( ) Diagnostic Test

t

d

iit

d

iittt xeecme

1110

t

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

time series 02

Documents

stationary

price index

series

data

damps

tpii

lag

yt