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TIME SERIES PROBLEM DO ALL SUB PARTS FOR FULL POINTS THANK YOU USE R OR R STUDIO

ID: 1719718 • Letter: T

Question

TIME SERIES PROBLEM DO ALL SUB PARTS FOR FULL POINTS THANK YOU USE R OR R STUDIO

Let {e_t} be a zero mean white noise process. Suppose that the observed process is Y_t = e_t + thetae_t-1. Find the autocorrelation function for {Y_t} when theta = 4 and when theta = 1/4. Is {Y_t} stationary? Show that the autocorrelation is the same for theta = v and for theta = l/v, for u 0. For simplicity, assume that the process mean is known to be zero and the variance of Y_t is known to be 1. You observe the series {Y_t} for t = 1,2,..., n and suppose that you can produce good estimates of the autocorrelations p_k. Do you think that you could determine which value of theta is correct (4 or 1/4) based on the estimate of p_k? Why or why not? Simulate from the process using each value of theta and the same white noise sequence, plot the simulations and the sample ACF, and comment with respect to part (c).

Explanation / Answer

B) i) x11 – 2x =0

ddx - 2x = 0

d2x - 2 x = o dx

dx - 2 x2/2 = c1

x1- 2x2/2= C1.

d (dx ) - 2x =0

d(dx) - 2x dx = 0 dx

dx - 2x2/2 = c1

x1 - 2x2/2 = c1

V0 = C1

c1 = 0