Question: The first one is given by the formula: where is an i.i.d N(0, 4) distributed sequence. The second process is given by: Pt Pt-1

The first one is given by the formula: where is an i.i.d

The first one is given by the formula: where is an i.i.d N(0, 4) distributed sequence. The second process is given by: Pt Pt-1 + Et - Et-1; where e follows a random walk: Tt Tt-1+ Et, Et = l + Et 1 + nt, where nt is an i.i.d N(0, 1) distributed sequence, cov (nt, et-k) = 0 for all t, and k. 1. Compute theoretical mean, and variance for both processes pt and rt. Is any of the processes stationary in terms of mean and variance? Which process has a constant variance?] 2. Compute Cov(tt, Et-1) for both processes. 3. Simulate 1000 realizations of length 500 for both processes pt and r+ (i.e. simulate a random realization of each process of length T = 500, repeat 1000 times) with following parameters =1, Po = To = 25, = 0. Plot the results, and comment please. Compute (analytically) P200, and r400.

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