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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)
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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
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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?
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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)
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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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© Roy Batchelor 2000EVIEWS Tutorial 17
Specific model:stage two
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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
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1-month ahead changes in lft500:actual v. forecast
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1111
© 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
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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
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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?