Consider two processes xt = wt and yt = xtD + vt where wt and vt are independent white noise processes with common variance 2,

Consider two processes xt = wt and yt = φxt−D + vt where wt and vt are independent white noise processes with common variance

σ2, φ is a constant, and D is a fixed integer delay.

(a) Compute the coherency between xt and yt.

(b) Simulate n = 1024 normal observations from xt and yt for φ = .9, σ2 = 1, and D = 0. Then estimate and plot the coherency between the simulated series for the following values of L and comment:

(i) L = 1, (ii) L = 3, (iii) L = 41, and (iv) L = 101.

Section 4.7