Data Analysis & Forecasting Faculty of Development Economics

Phung Thanh Binh (2010)

TIME SERIES ANALYSIS BASIC REGRESSION MODELS

In time series regression analysis, we often face the following cases (of which breaks are sometimes considered in the forms of structural dummy variables or interaction variables with these models)

CASE 1 If we have Yt : I(0) Xt : I(0)

� Standard OLS is normally applied. � But this rarely occurs in economic

data

CASE 2 If we have Yt : I(1) Xt : I(1) Yt and Xt are NOT cointegrated. � Standard OLS is invalid. � Two possibilities: (1) Estimate elasticities: GLS (2) Investigate ‘short-run’ causality:

Standard version of Granger causality/Static Granger causaulity (weak Granger causality test only)

� This has been widely applied in empirical studies.

CASE 3 If we have Yt : I(1) Xt : I(1) Yt and Xt are cointegrated. � Standard OLS is still valid for long-run

relationship analysis. � Two possibilities: (1) Investigate ‘short-run’/‘weak’ causality:

Standard version of granger causality/Static Granger Causality

(2) Investigate both ‘short-run’ and ‘long-run’ causality: Cointegration & error correction (ECM) version of Granger causality/Dynamic Granger causality (speed of adjustment and strong Granger casusality test)

� This has been widely applied in empirical studies.

CASE 4 If we have Yt : I(d) Xt : I(d’) where d ≠ d’ irrespestive of Yt and Xt are cointegrated or non-cointegrated. � Standard OLS is invalid. � Both ‘standard’ and ‘ECM’

versions of Granger causality are not applicable.

� Two widely accepted methods for analysing causality are:

(1) Toda & Yamamoto (or Augmented) version of Granger causality (rarely used until now)

(2) ARDL Models (*) � These methods have recently

applied in empirical studies. * The bounds test for cointegration within ARDL has a special link with ECM, this is also called as VECM.