Cointegration and error correction

Transcription

1 EVIEWS tutorial: Cointegration and error correction Professor Roy Batchelor City University Business School, London & ESCP, Paris EVIEWS Tutorial 1 EVIEWS On the City University system, EVIEWS 3.1 is in Start/ Programs/ Departmental Software/CUBS Analysing stationarity in a single variable using VIEW Analysing cointegration among a group of variables Estimating an ECM model Estimating a VAR-ECM model EVIEWS Tutorial 2 1 1

2 The FT500M workfile EVIEWS Tutorial 3 Data transformation Generate a series for the natural log of the FT500 index (lft500) Test for stationarity in the level of this series the first difference of this series (dlft500) Results show that lft500 is an I(1) variable EVIEWS Tutorial 4 2 2

3 Generate ln(ft500) EVIEWS Tutorial 5 Augmented Dickey-Fuller (ADF) Test EVIEWS Tutorial 6 3 3

4 ADF results: level The hypothesis that lft500 has a unit root cannot be be rejected EVIEWS Tutorial 7 ADF test results: first difference The hypothesis that the the first difference of of lft500 has a unit root can be be rejected. So So lft500 is is I(1) EVIEWS Tutorial 8 4 4

5 Cointegration: two variables The variables lft500 (log of stock index) and ldiv (log of dividends per share) are both I(1) 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) The expression in brackets [] is called the cointegrating vector, which has normalised coefficients [ 1, -a 0, -a 1 ] EVIEWS Tutorial 9 Form new group... EVIEWS Tutorial

6 Common trends? EVIEWS Tutorial 11 Engle-Granger: first stage regression Don t worry about this... EVIEWS Tutorial

7 Save first-stage residuals (u t = RES) EVIEWS Tutorial 13 Engle-Granger:stage two (ECM) regression About 7% of of disequilibrium corrected each month EVIEWS Tutorial

8 General model: stage one (I(1) variables) EVIEWS Tutorial 15 General model: stage two EVIEWS Tutorial

9 Specific model:stage two EVIEWS Tutorial 17 1-month ahead forecasts of lft500 from first stage regression EVIEWS Tutorial

10 1-month ahead forecasts of dlft500 from the second stage ECM EVIEWS Tutorial 19 1-month ahead changes in lft500: actual v. forecast EVIEWS Tutorial

11 Johansen method: make group of associated I(1) variables (lft500, ldiv) EVIEWS Tutorial 21 Set up Johansen procedure EVIEWS Tutorial

12 Johansen test for cointegrating vector(s) EVIEWS Tutorial 23 Cointegrating vector (cf. First stage regression) EVIEWS Tutorial

13 Set up VAR-ECM EVIEWS Tutorial 25 Cointegrating vector of both endogenous I(1) variables EVIEWS Tutorial

14 VAR-ECM-X models for both endogenous variables About About 2% 2% of of disequilibrium corrected each each month month by by changes changes in in dividends ldiv ldiv Exogenous I(0) I(0) variables affecting stock stock index index and and dividends About About 10% 10% of of disequilibrium corrected each each month month by by changes changes in in stock stock index index lft500 lft500 EVIEWS Tutorial 27 Forecasting: make VAR-ECM model EVIEWS Tutorial

15 Dynamic forecasting: 1 year ahead EVIEWS Tutorial 29 Stock index and dividend forecasts, 1996 EVIEWS Tutorial

16 Updated model ( ) EVIEWS Tutorial 31 Forecasts for : a Crash coming? EVIEWS Tutorial