Let et~IID N(0,1) and define Xt=etet-1. Show that {Xt} is a white noise sequence. This provides an example of a dependent white noise sequence. Two bonus points for rigorously proving Xt and Xt+1 are not independent.
Let Xt=1+et-0.5et-1, t=1,2,3,..., where et~IID N(0,2), the variance of et is 2.
a. Compute the mean of Xt.
b. Compute the variance of Xt.
c. Find the correlation between Xt and et-1.