Question

Suppose that a stationary time series, {Y], has an autocorrelation function of the form ρ,-φκ for k > 0, where φ is a constant in the range (-1,+1) (a) Show that Var(Y)--LT n(1-ф) (Hint: Use Equation (3.2.3) on page 28, the finite geometric sum and the related sum (b) If n is large, argue that Var()- (C) Plot ( 1 + φ)/(1-0) for φ over the range-l to +1. Interpret the plot in terms 1n of the precision in estimating the process mean.