Question

5. Suppose a stationary time series {Xt}t in Z with mean 0 and autocorrelation func tion p(h) = corr(Xt+h, Xt), for h in Z. Show that the best linear predictor of Xn+h of the form aXn is obtained with a =p(h). That is, the function S(a) = E[(Xn+h − aXn)2] is minimised with a =p(h). [Total 10 marks]

Name: 5 suppose a stationary time series xtt in z with mean 0 and autocorrelation func tion ph corrxth xt for h in z show that the best linear predictor of xnh of the form axn is obtained with a p 59892
Uploaded: 2023-02-06T14:13:02-08:00
Duration: 1 min 26 s
Channel: Madhur L
Description: 5 suppose a stationary time series xtt in z with mean 0 and autocorrelation func tion ph corrxth xt for h in z show that the best linear predictor of xnh of the form axn is obtained with a p 59892

          5. Suppose a stationary time series {Xt}t in Z with mean 0 and autocorrelation func tion  p(h) = corr(Xt+h, Xt), for h  in  Z. Show that the best linear predictor of Xn+h of the form aXn is obtained with a =p(h). That is, the function S(a) = E[(Xn+h − aXn)2] is minimised with a =p(h). 
[Total 10 marks]

Added by Rosario T.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

02/06/2023

Step 1

We need to minimize the function S(a) = E[(Xn+h − aXn)2] with respect to the parameter a. Show more…

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5. Suppose a stationary time series {Xt}t in Z with mean 0 and autocorrelation func tion p(h) = corr(Xt+h, Xt), for h in Z. Show that the best linear predictor of Xn+h of the form aXn is obtained with a =p(h). That is, the function S(a) = E[(Xn+h − aXn)2] is minimised with a =p(h). [Total 10 marks]