Question: Consider a linear process Xt = 1X j=0 cj utj ; 1X j=0 jcj j < 1 (3) 1 where (ut; Ft) is a martingale

Consider a linear process Xt = 1X j=0 cj utj ; 1X j=0 jcj j < 1 (3) 1 where (ut; Ft) is a martingale dierence sequence with E (u2 t j Ft1) = 2 for all t. Show that E (Xt) = 0 and compute the covariance (k) := cov (Xt; Xtk) = E (XtXtk) when k 0 and when k < 0. Show that (k) is independent of t and that (k) = (k) for all k 0

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