# Solving for 6 and 6 à we obtain 2 time series

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Solving for6¿and6À, we obtain
2TIME SERIES ANALYSIS6¿=−1À1 + 1À+ 17, 6À=1¶1 + 1À¹1 + 1À+ 17.So, the desired best linear estimate is1À1 + 1À+ 17°¿+1¶1 + 1À¹1 + 1À+ 17°À.(b)Write the best linear estimate as³¿°7+ ³À°8. Then,³¿and³Àare determined byÄ½¶0¹½¶1¹½¶1¹½¶0¹Å "³¿³À# = Ä½¶1¹½¶2¹Å.Similar to the arguments in part (a), we obtain³¿=1¶1 + 1À¹1 + 1À+ 17, ³À=−1À1 + 1À+ 17.So, the desired best linear estimate is1¶1 + 1À¹1 + 1À+ 17°71À1 + 1À+ 17°8.(c)Write the best linear estimate as6Àare
3TIME SERIES ANALYSISThe MSE for the estimate in part (b) is the same:0À¶1 + 1À¹¶1 + 17¹1 + 1À+ 17,On the other hand, the MSE for the estimate in part (c) is smaller:

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