The unrestricted model is the following adl11 model

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Unformatted text preview: − ρβ2 Xt −1 + εt 44 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables Going back to lagged dependent variables Yt = β1 + β2 Xt + β3 Yt −1 + ρut −1 + εt Yt −1 = β1 + β2 Xt −1 + β3 Yt −2 + ut −1 Subtract ρ times the second equation from the first and we get after rearranging: Yt = β1 − ρβ1 + ρYt −1 + β2 Xt − ρβ2 Xt −1 + β3 Yt −1 − ρβ3 Yt −2 + εt Nonlinear estimation method is usually used. 45 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables Going back to lagged dependent variables Yt = β1 + β2 Xt + β3 Yt −1 + ρut −1 + εt Yt −1 = β1 + β2 Xt −1 + β3 Yt −2 + ut −1 Subtract ρ times the second equation from the first and we get after rearranging: Yt = β1 − ρβ1 + ρYt −1 + β2 Xt − ρβ2 Xt −1 + β3 Yt −1 − ρβ3 Yt −2 + εt Nonlinear estimation method is usually used. 46 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables Going back to lagged dependent variables Yt = β1 + β2 Xt + β3 Yt −1 + ρut −1 + εt Yt −1 = β1 + β2 Xt −1 + β3 Yt −2 + ut −1 Subtract ρ times the second equation from the first and we get after rearranging: Yt = β1 − ρβ1 + ρYt −1 + β2 Xt − ρβ2 Xt −1 + β3 Yt −1 − ρβ3 Yt −2 + εt Nonlinear estimation method is usually used. 47 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Lagged Dependent Variables Going back to lagged dependent variables Yt = β1 + β2 Xt + β3 Yt −1 + ρut −1 + εt Yt −1 = β1 + β2 Xt −1 + β3 Yt −2 + ut −1 Subtract ρ times the second equation from the first and we get after rearranging: Yt = β1 − ρβ1 + ρYt −1 + β2 Xt − ρβ2 Xt −1 + β3 Yt −1 − ρβ3 Yt −2 + εt Nonlinear estimation method is usually used. 48 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Common Factor Test The transformation we made to remove autocorrelation resulted in the following equation Yt = β1 − ρβ1 + ρYt −1 + β2 Xt − ρβ2 Xt −1 + εt Remember that this is a restricted model. The unrestricted model is the following ADL(1,1) model: Yt = λ1 + λ2 Yt −1 + λ3 Xt + λ4 Xt −1 + εt What are the restrictions? restriction on parameters: λ4 = −λ2 λ3 interpretation of λ2 if the restriction is valid. If not, no specific meaning. Can we test that the restrictions hold? 49 / 62 Introduction Time Series and OLS Two Dynamic Models Autocorrelation Assumption C7 Autocorrelation Detection Lagged Dependent Common Factor Test The transformation we made to remove autocorrelation resulted in the following equation Yt = β1 − ρβ1 + ρYt −1 + β2 Xt − ρβ2 X...
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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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