STA457H1 Lecture : 2.5 Forecasting.docx
Document Summary
We want to find the best linear combination a0+a1w 1+a2w 2+ +an w n error (mse) of e[(u (a0+a1 w 1+a2 w 2+ +anw n))2] is minimized such that the mean squared. P (u w )=e[u ]+ at ( w e[ w ]) where cov ( w ) a=cov (u , w ) is non singular, then. A=[cov ( w )] 1cov (u , w ) E[(u p (u w )) w ]=0 and e[u p (u w )]=0. Proof: note p (u w )=e[u ]+ at ( w e[ w ]) Hence u p (u w )=u e [u ] at ( w e [ w ])=u w . E[(u p (u w )) w ]=e[(u at w ) w ]=e [u w ] at e[ w w ] At ( w e [ w ])=e[ w w t a]=e[ w w 8t] a.
