A moving average of order 1 is defined as:

Xt = Zt + Zt1 where (Zt)tN is a white noise with = 1 and is an unknown parameter.

Take = 4/ 10

a) Write a code to simulate a moving average process with = 4/10 driven

by a Gaussian white noise. Show a graph with the simulated values.

b) Write a code to simulate a moving average process with = 4/10 driven

by a white noise following a distribution t-student with 4 degrees of freedom.

c) Compute the empirical autocorrelation function of both processes, i.e. moving average processes with Gaussian and student noises. Show the graphs of the autocorrelations. What is the meaning of X (1)?

d) Compute the theoretical mean, variance and autocorrelation functions for both processes. Show your steps.

e) Are the processes stationary in the strict and wide? Explain.