1 1 © Roy Batchelor 2000EVIEWS Tutorial 1 EVIEWS tutorial: Cointegration and error correction Professor Roy Batchelor City University Business School, London & ESCP, Paris © Roy Batchelor 2000EVIEWS Tutorial 2 EVIEWS r On the City University system, EVIEWS 3.1 is in Start/ Programs/ Departmental Software/CUBS r Analysing stationarity in a single variable using VIEW r Analysing cointegration among a group of variables r Estimating an ECM model r Estimating a VAR-ECM model 2 2 © Roy Batchelor 2000EVIEWS Tutorial 3 The FT500M workfile © Roy Batchelor 2000EVIEWS Tutorial 4 Data transformation r Generate a series for the natural log of the FT500 index (lft500) r Test for stationarity in – the level of this series – the first difference of this series (dlft500) r Results show that lft500 is an I(1) variable 3 3 © Roy Batchelor 2000EVIEWS Tutorial 5 Generate ln(FT500) © Roy Batchelor 2000EVIEWS Tutorial 6 Augmented Dickey-Fuller (ADF) Test 4 4 © Roy Batchelor 2000EVIEWS Tutorial 7 ADF results: level The hypothesis that lft500 has a unit root cannot be rejected The hypothesis that lft500 has a unit root cannot be rejected © Roy Batchelor 2000EVIEWS Tutorial 8 ADF test results: first difference The hypothesis that the first difference of lft500 has a unit root can be rejected. So lft500 is I(1) The hypothesis that the first difference of lft500 has a unit root can be rejected. So lft500 is I(1) 5 5 © Roy Batchelor 2000EVIEWS Tutorial 9 Cointegration: two variables r The variables lft500 (log of stock index) and ldiv (log of dividends per share) are both I(1) r We can test whether they are cointegrated – that is, whether a linear function of these is I(0) – An example of a linear function is lft500 t = a 0 + a 1 ldiv t + u t when u t = [lft500 t - a 0 - a 1 ldiv] might be I(0) r The expression in brackets [] is called the cointegrating vector, which has normalised coefficients [ 1, -a 0 , -a 1 ] © Roy Batchelor 2000EVIEWS Tutorial 10 Form new group 6 6 © Roy Batchelor 2000EVIEWS Tutorial 11 Common trends? © Roy Batchelor 2000EVIEWS Tutorial 12 Engle-Granger: first stage regression Don’t worry about this Don’t worry about this 7 7 © Roy Batchelor 2000EVIEWS Tutorial 13 Save first-stage residuals (u t = RES) © Roy Batchelor 2000EVIEWS Tutorial 14 Engle-Granger:stage two (ECM) regression About 7% of disequilibrium “corrected” each month About 7% of disequilibrium “corrected” each month 8 8 © Roy Batchelor 2000EVIEWS Tutorial 15 General model: stage one (I(1) variables) © Roy Batchelor 2000EVIEWS Tutorial 16 General model: stage two 9 9 © Roy Batchelor 2000EVIEWS Tutorial 17 Specific model:stage two © Roy Batchelor 2000EVIEWS Tutorial 18 1-month ahead forecasts of lft500 from first stage regression 10 10 © Roy Batchelor 2000EVIEWS Tutorial 19 1-month ahead forecasts of dlft500 from the second stage ECM © Roy Batchelor 2000EVIEWS Tutorial 20 1-month ahead changes in lft500: actual v. forecast [...]... ldiv) EVIEWS Tutorial 21 © Roy Batchelor 2000 Set up Johansen procedure EVIEWS Tutorial 22 © Roy Batchelor 2000 11 11 Johansen test for cointegrating vector(s) EVIEWS Tutorial 23 © Roy Batchelor 2000 Cointegrating vector (cf First stage regression) EVIEWS Tutorial 24 © Roy Batchelor 2000 12 12 Set up VAR-ECM EVIEWS Tutorial 25 © Roy Batchelor 2000 Cointegrating vector of both endogenous I(1) variables EVIEWS. .. Batchelor 2000 Forecasting: make VAR-ECM model EVIEWS Tutorial 28 © Roy Batchelor 2000 14 14 Dynamic forecasting: 1 year ahead EVIEWS Tutorial 29 © Roy Batchelor 2000 Stock index and dividend forecasts, 1996 EVIEWS Tutorial 30 © Roy Batchelor 2000 15 15 Updated model (1975-98) EVIEWS Tutorial 31 © Roy Batchelor 2000 Forecasts for 1999-2000: a Crash coming? EVIEWS Tutorial 32 © Roy Batchelor 2000 16 16 ... variables EVIEWS Tutorial 26 © Roy Batchelor 2000 13 13 VAR-ECM-X models for both endogenous variables About 2% of About 2% of disequilibrium disequilibrium “corrected” each month “corrected” each month by changes in dividends by changes in dividends ldiv ldiv Exogenous I(0) Exogenous I(0) variables variables affecting stock affecting stock index and index and dividends dividends EVIEWS Tutorial 27 About . 1 1 © Roy Batchelor 200 0EVIEWS Tutorial 1 EVIEWS tutorial: Cointegration and error correction Professor Roy Batchelor City University. Batchelor 200 0EVIEWS Tutorial 5 Generate ln(FT500) © Roy Batchelor 200 0EVIEWS Tutorial 6 Augmented Dickey-Fuller (ADF) Test 4 4 © Roy Batchelor 200 0EVIEWS Tutorial