Drift from naive expectations

(a) Prove Proposition 6A.2 for the AR(1) case and extend it to a general stationary process with autocorrelations $\rho_k$. (b) With an earnings response coefficient of $c$ = 1.5% per unit SUE and $\phi = 0.35$, compute the expected return at the next announcement per unit SUE, and the expected top-minus-bottom decile spread of that return when SUE is standard normal. (c) Suppose instead the lag-1 to lag-4 autocorrelations of seasonal differences are $0.35, 0.20, 0.08, -0.25$ (illustrative, with the sign pattern Bernard and Thomas report). Compute the expected sum of the next four announcement returns per unit SUE, and the corresponding decile spread. (d) Explain why a negative lag-4 autocorrelation is natural for seasonal differences, and what it implies for a strategy that holds for a full year.