Page 28 - Contributed Paper Session (CPS) - Volume 1

CPS658 Sagaren P.
there are deterministic co-integrated relationships among variables-
deterministic terms in the Var(p) model are not present in the VECM(p) form.
(2) If there are stochastic co-integrated relationships in the Var(p) model,
deterministic terms appear as the VECM(p) form in the EC term or as an
independent term in the VECM(p) form.

4. Data Analysis
Based on the results of the of the Augmented Dickey Fuller (ADF) unit root
test both series have a unit root and are first order difference stationary. The
results show that both series are I (1) processes. To test for co-integration,
Johansen's test was used. The maximum lag length was set to 7 quarters and
an autoregressive order of p=2 was selected based on the minimum
information criterion.Both series were found to be co-integrated with rank=1.
The next step was to investigate the model specification for the 5 cases below.
Case 1: If there is no separate drift in the VECM(p) form then the model is
given by:
′
Δ = −1 + Δ −1 +. . . + −1 Δ −+1 + from (2)

1

Case 2:
Suppose there is no separate drift in the VECM(p) form, but a constant
0
enters only via the error correction term.
Consider the K-dimensional Var(p) process where is K×1 and = +

Suppose  =  are fixed K-dimensional parameter vectors. Then
0
′
∆ = −1 + Δ −1 +. . . + Δ −+1 +

1
′
= ( −1 − ) + Δ −1 +. . . + Δ −+1 +

1
0
′
′
= −1 − + Δ −1 +. . . + Δ −+1

0
1
′
= −1 + Δ −1 +. . . + Δ −+1 +
0+ 1

where = − is the restriction of the intercept.
′
0
0
Case 3:
There is a separate drift  and no separate linear trend in the VECM(p) form
0
the following model is used.
′
∆ = −1 + Δ −1 +. . . + Δ −+1 +

1

Case 4:
There is a separate drift and no separate linear trend in the VECM(p) form, but
a linear trend enters only via the error correction term.
If = + is a linear trend, we have = −
1

0
1

= − − and Δ = Δ − Δ( − −1 )
0

0

1

′
Therefore from (3) ∆ = −1 + Δ −1 +. . . + −1 Δ −+1 +
1

Substitute = − ; Δ −1 = Δ −1 − ; and = − −
1
1

0
1

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