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© Roy Batchelor 2000EVIEWS Tutorial 1

EVIEWS tutorial:Cointegration and error correction

Professor Roy BatchelorCity University Business School, London& ESCP, Paris

© Roy Batchelor 2000EVIEWS Tutorial 2

EVIEWS

r On the City University system, EVIEWS 3.1 is inStart/ 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

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© 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

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© Roy Batchelor 2000EVIEWS Tutorial 5

Generate ln(FT500)

© Roy Batchelor 2000EVIEWS Tutorial 6

Augmented Dickey-Fuller (ADF) Test

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© Roy Batchelor 2000EVIEWS Tutorial 7

ADF results: level

The hypothesis thatlft500 has a unit rootcannot be rejected

The hypothesis thatlft500 has a unit rootcannot be rejected

© Roy Batchelor 2000EVIEWS Tutorial 8

ADF test results: first difference

The hypothesis thatthe first difference oflft500 has a unit rootcan be rejected.

So lft500 is I(1)

The hypothesis thatthe first difference oflft500 has a unit rootcan be rejected.

So lft500 is I(1)

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© Roy Batchelor 2000EVIEWS Tutorial 9

Cointegration: two variables

r The variables lft500 (log of stock index) and ldiv (log ofdividends 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

lft500t = a0 + a1ldivt + ut

when ut = [lft500t - a0 - a1ldiv] might be I(0)

r The expression in brackets [] is called the cointegrating vector,which has normalised coefficients [ 1, -a0 , -a1 ]

© Roy Batchelor 2000EVIEWS Tutorial 10

Form new group ...

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© Roy Batchelor 2000EVIEWS Tutorial 11

Common trends?

© Roy Batchelor 2000EVIEWS Tutorial 12

Engle-Granger: first stage regression

Don’t worryabout this...Don’t worryabout this...

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© Roy Batchelor 2000EVIEWS Tutorial 13

Save first-stage residuals (ut = RES)

© Roy Batchelor 2000EVIEWS Tutorial 14

Engle-Granger:stage two (ECM) regression

About 7% ofdisequilibrium

“corrected” eachmonth

About 7% ofdisequilibrium

“corrected” eachmonth

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© Roy Batchelor 2000EVIEWS Tutorial 15

General model: stage one (I(1) variables)

© Roy Batchelor 2000EVIEWS Tutorial 16

General model: stage two

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Specific model:stage two

© Roy Batchelor 2000EVIEWS Tutorial 18

1-month ahead forecasts of lft500 from firststage regression

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© Roy Batchelor 2000EVIEWS Tutorial 19

1-month ahead forecasts of dlft500 fromthe second stage ECM

© Roy Batchelor 2000EVIEWS Tutorial 20

1-month ahead changes in lft500:actual v. forecast

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© Roy Batchelor 2000EVIEWS Tutorial 21

Johansen method: make group ofassociated I(1) variables (lft500, ldiv)

© Roy Batchelor 2000EVIEWS Tutorial 22

Set up Johansen procedure

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© Roy Batchelor 2000EVIEWS Tutorial 23

Johansen test for cointegrating vector(s)

© Roy Batchelor 2000EVIEWS Tutorial 24

Cointegrating vector (cf. First stageregression)

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Set up VAR-ECM

© Roy Batchelor 2000EVIEWS Tutorial 26

Cointegrating vector of both endogenousI(1) variables

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© Roy Batchelor 2000EVIEWS Tutorial 27

VAR-ECM-X models for both endogenousvariables

About 10% ofdisequilibrium

“corrected” each monthby changes in stock

index lft500

About 10% ofdisequilibrium

“corrected” each monthby changes in stock

index lft500

About 2% ofdisequilibrium

“corrected” each monthby changes in dividends

ldiv

About 2% ofdisequilibrium

“corrected” each monthby changes in dividends

ldiv

Exogenous I(0)variables

affecting stockindex anddividends

Exogenous I(0)variables

affecting stockindex anddividends

© Roy Batchelor 2000EVIEWS Tutorial 28

Forecasting: make VAR-ECM model

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Dynamic forecasting: 1 year ahead

© Roy Batchelor 2000EVIEWS Tutorial 30

Stock index and dividend forecasts, 1996

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© Roy Batchelor 2000EVIEWS Tutorial 31

Updated model (1975-98)

© Roy Batchelor 2000EVIEWS Tutorial 32

Forecasts for 1999-2000: a Crash coming?