32 62 introduction time series and ols two dynamic

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Unformatted text preview: t = ρut −1 + εt MA(1): ut = εt + λεt −1 28 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Autocorrelation There are two main types of autocorrelation: AR(p): ut = ρ1 ut −1 + · · · + ρp ut −p + εt MA(q): ut = εt + λ1 εt −1 + · · · + λq εt −q but we will mainly focus on the special cases AR(1): ut = ρut −1 + εt MA(1): ut = εt + λεt −1 29 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Detection How do we detect autocorrelation in the error term of a model? 1 2 3 Graph of residuals Durbin Watson Durbin H (when?) 1: Graph of residuals 30 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Detection 2: Durbin Watson Test for AR(1) Yt = β1 + β2 Xt + ut ut = ρut −1 + εt d = T 2 t =2 (et − et −1 ) T 2 t =1 et In large samples d → 2 − 2ρ. 31 / 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. 32 / 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. 33 / 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...
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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).

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