Consider a random walk (left{y_{t} ight}) as the partial sum of a white noise process (left{c_{t} ight}).
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Consider a random walk \(\left\{y_{t}\right\}\) as the partial sum of a white noise process \(\left\{c_{t}\right\}\).
a. Show that the \(l\)-step forecast error is \(y_{T+l}-\widehat{y_{T+l}}=\sum_{j=1}^{l}\left(c_{T+j}-\bar{c}\right)\).
b. Show that the approximate variance of the \(l\)-step forecast error is \(l \sigma_{c}^{2}\).
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Related Book For
Regression Modeling With Actuarial And Financial Applications
ISBN: 9780521135962
1st Edition
Authors: Edward W. Frees
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