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Unformatted text preview: of the coefﬁcient of the lagged dependent
variable Yt −1 . In general, ρ can be obtained by the relationship
ˆ
d → 2 − 2ρ.
34 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation
Assumption C7 Autocorrelation Detection Lagged Dependent Detection
3: Durbin H Test
We use this test when we have lagged dependent variables.
The Durbin Watson test is biased towards 2 in this situation
what does this mean?
Increase the risk of a Type II error. That is, even though there is
autocorrelation, we fail to reject the null hypothesis that there is
no autocorrelation.
h=ρ n
2
1 − nsbY (−1) 2
ρ is an estimate of ρ in the AR(1) process, sbY (−1) is an estimate
ˆ
of the variance of the coefﬁcient of the lagged dependent
variable Yt −1 . In general, ρ can be obtained by the relationship
ˆ
d → 2 − 2ρ.
35 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation
Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables
The presence of lagged dependent variables makes OLS
estimates biased in ﬁnite samples. But they are still consistent.
But if there is autocorrelation in the errors then we have
inconsistency as well. Yt = β1 + β2 Xt + β3 Yt −1 + ut ut = ρut −1 + εt ε is iid. What is the source of inconsistency? ⇒ Yt −1 and ut are
not independent. Can we use the Durbin Watson test to detect
autocorrelation? What do we do instead?
36 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation
Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables
The presence of lagged dependent variables makes OLS
estimates biased in ﬁnite samples. But they are still consistent.
But if there is autocorrelation in the errors then we have
inconsistency as well. Yt = β1 + β2 Xt + β3 Yt −1 + ut ut = ρut −1 + εt ε is iid. What is the source of inconsistency? ⇒ Yt −1 and ut are
not independent. Can we use the Durbin Watson test to detect
autocorrelation? What do we do instead?
37 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation
Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables
The presence of lagged dependent variables makes OLS
estimates biased in ﬁnite samples. But they are still consistent.
But if there is autocorrelation in the errors then we have
inconsistency as well. Yt = β1 + β2 Xt + β3 Yt −1 + ut ut = ρut −1 + εt ε is iid. What is the source of inconsistency? ⇒ Yt −1 and ut are
not independent. Can we use the Durbin Watson test to detect
autocorrelation? What do we do instead?
38 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation
Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables
The presence of lagged dependent variables makes OLS
estimates biased in ﬁnite samples. But they are still consistent.
But if there is autocorrelation in the errors then we have
inconsistency as well. Yt = β1 + β2 Xt + β3 Yt −1 + ut ut = ρut −1 + εt ε is iid. What is the source of inconsistency? ⇒ Yt −1 and ut are
no...
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This document was uploaded on 03/12/2014 for the course ECON 202 at University of London University of London International Programmes (Distance Learning).
 Spring '13
 ChristopherDougherty
 Econometrics

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