EVIEWS tutorial Cointegration and error correction potx

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© 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
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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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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)
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© 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

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© 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
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© 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
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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 first
stage regression
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© 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
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© Roy Batchelor 2000EVIEWS Tutorial 21
Johansen method: make group of
associated 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 stage

regression)
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© Roy Batchelor 2000EVIEWS Tutorial 25
Set up VAR-ECM
© Roy Batchelor 2000EVIEWS Tutorial 26
Cointegrating vector of both endogenous
I(1) variables
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© Roy Batchelor 2000EVIEWS Tutorial 27
VAR-ECM-X models for both endogenous
variables
About 10% of
disequilibrium
“corrected” each month
by changes in stock
index lft500
About 10% of
disequilibrium
“corrected” each month
by changes in stock
index lft500
About 2% of
disequilibrium
“corrected” each month
by changes in dividends
ldiv
About 2% of
disequilibrium

“corrected” each month
by changes in dividends
ldiv
Exogenous I(0)
variables
affecting stock
index and
dividends
Exogenous I(0)
variables
affecting stock
index and
dividends
© Roy Batchelor 2000EVIEWS Tutorial 28
Forecasting: make VAR-ECM model
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© Roy Batchelor 2000EVIEWS Tutorial 29
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?