Applied Econometric Time-Series Data Analysis

Types of Data Time series data Cross-sectional data Panel data 1 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. Cross-sectional data 2 Panel data 3

The Procedure to Analysis Economic or Financial Theory Summary Statistics of Data Basic Econometric Advanced Econometric Luukkonen et al. (1988) Linearity Test not reject If reject Linear Model Nonlinear Model

The Procedure to Analysis Time Series Data Unit Root Test Non-Stationarity Dickey-Fuller Staionaruty Augmented DF Orders of Integration H0: Yt ~ I(1) H1: Yt ~ I(0) VAR in Level The same Difference Phillips-Perron E-G J-J H-I KPSS ARDL Bounding Test DF-GLS, NP H0: Yt ~ I(0) H1: Yt ~ I(1) KPSS Cointegration Test

The Procedure to Analysis Unit Root Test Staionaruty Cointegration Test Yes No EG,JJ, KPSS ARDL VAR in Level VECM UECM (Pesaran et al., 2001) VAR in differ Model Specification

The Procedure to Analysis Model Estimation Economic or Finance Implication Impulse Resp Variance Dec Granger Causality

The Procedure to Analysis Goodness-of-fit R square Error specification Ramsey’s RESET sationarity CUSUM (square) Series autocorrelation Ljung-Box Q, Q2 Heteroskedastic ACH-LM Teat Normality Jarque-Bera N Diagnostic Checking

Econometric Soft Packages EViews Rats GAUSS Matlab Microfit EasyReg STATA TSP

National Statistic, ROC 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, ROC 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

Currency exchange rate 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

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) Moving Average, MA (1)

Stationary Time Series Box-Jenkins (1976) ARMA (p, q) model The necessary and sufficient stationarity condition

Stationary Time Series The determination of the order of an ARMA process Autocorrelation function (ACF) Partial ACF (PACF) Ljung-Box Q statistic

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 ARMA(p, q)

Stationary Time Series e series is AR(1) P* = 1

Non-stationary Time Series Autoregressive integrated moving average (ARIMA) model If Y series is explosive 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

Non-stationary Time Series Unit Root Test ADF Test KPSS De-data De-trend De-mean

Non-stationary Time Series Selection Criteria of the Lag Length Schwartz Bayesian Criterion (SBC) Akaike Information Criterion (AIC) Small sample Big sample sum of squared residuals observations parameters

Non-stationary Time Series Reject H0

Non-stationary Time Series Engle-Granger 2-Stage Cointegration Test Step 1: regress real exchange rate Step 2: error term Hypothesis ADF Unit Root Test If reject H0, We support PPP

Non-stationary Time Series Name as ppp

Non-stationary Time Series Error – Correction Model (ECM) Where x is independent variables Residual ( ) Diagnostic Test

Non-stationary Time Series

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