In: Statistics and Probability
1. Consider the process {Xt} in which Xt =
Zt + 0.5Zt-1 - 2Zt-2. Investigate
the
stationarity of the process under the following conditions.
Calculate the ACF for the
stationary models.
(a) Zt ~ WN(0,(sigma)2) ; (sigma)2 <
infinity
(b) {Zt } is a sequence of i.i.d random variables with
the following distribution:
fzt(z) = 2/z3 ; z > 1