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# 6 30 y a utocorrelation x 7 30 c onsequences of

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Unformatted text preview: r choice of speciﬁcation (as opposed to pure autocorrelation). 6 / 30 Y A UTOCORRELATION X 7 / 30 C ONSEQUENCES OF AUTOCORRELATION Estimated coefﬁcients (β ) remain unbiased and consistent Variance of β increases serially correlated error term causes the dependent variable to ﬂuctuate in a way that the OLS estimation procedure attributes to the independent variable OLS tend to underestimate the variance of β autocorrelation increases the variances of the estimates in a way that is masked by OLS estimates ⇒ The same consequences as for the heteroskedasticity 8 / 30 VARIANCE OF OLS UNDER AUTOCORRELATION Consider the model y = Xβ + ε Suppose that εt = ρεt−1 + ut OLS estimate is β= XX −1 Xy Variance of the estimate is Var β = X X where Ω = Var (ε) = −1 X ΩX X X σ2 ρ 0 ρ σ2 ρ 0 ρ σ2 . . . . . . . . . 000 ... ... ... .. . −1 0 0 0 . . . . . . σ2 , 9 / 30 D URBIN -WATSON TEST FOR AUTOCORRELATION Used to determine if there is a ﬁrst-order serial correlation by examining the residuals of the equation Assumptions (criteria for using this test): The regression includes the intercept If autocorrelation is present, it is of AR(1) type: εt = ρεt−1 + ut The regression does not include a lagged dependent variable 10 / 30 D URBIN -WATSON TEST FOR AUTOCORRELATION D...
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