Consider the ARDL ((2,1)) model with auxiliary AR(1) model (x_{t}=alpha+phi x_{t-1}+v_{t}), where (I_{t}=left{y_{t}, y_{t-1}, ldots, x_{t}, x_{t-1},
Question:
Consider the ARDL \((2,1)\) model
with auxiliary AR(1) model \(x_{t}=\alpha+\phi x_{t-1}+v_{t}\), where \(I_{t}=\left\{y_{t}, y_{t-1}, \ldots, x_{t}, x_{t-1}, \ldots\right\}, E\left(e_{t} \mid I_{t-1}\right)=0\), \(E\left(v_{t} \mid I_{t-1}\right)=0, \operatorname{var}\left(e_{t} \mid I_{t-1}\right)=\sigma_{e}^{2}, \operatorname{var}\left(v_{t} \mid I_{t-1}\right)=\sigma_{v}^{2}\), and \(v_{t}\) and \(e_{t}\) are independent. Assume that sample observations are available for \(t=1,2, \ldots, T\).
a. Show that the best forecasts for periods \(T+1, T+2\) and \(T+3\) are given by
b. Show that the variances of the forecast errors are given by
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Related Book For
Principles Of Econometrics
ISBN: 9781118452271
5th Edition
Authors: R Carter Hill, William E Griffiths, Guay C Lim
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