Question

Consider the 5 point running mean where ut ~ NID(0, σ ), and let σ -1. (i) Determine the theoretical auto-covariance (ACF) for v, and the theoretical cross-covariance function (CCF) between w and vt. (ii) Generate a realization of w of length 1000, compute the associated 5-point moving average v and plot these two time series on the same graph.i Calculate the corresponding sample versions for the ACF and CCF and remark on how these resemble and differ from the theoretical results. (iv) Repeat for another realization of length 1000 and remark on the similarities/differences

Answer 1

clc;
n=1000
w=normrnd(0,1,n,1);
for i=3:n-2
    v(i)=(sum(w(i-2:i+2)))/5;
end
plot(w,'r')
hold on     % hold on command is used to plot both w and v time series on same plot
plot(v,'b')
autocorr(v)
crosscorr(v,w)

$j+KxM5skJwjBgAAAABJRU5ErkJggg==$

Conclusion : here we can conclude from figures regenerated through samples that sample and theoretical autocovariance function is same