Time series question about intrinsically stationary processes
Time series question about intrinsically stationary processes 2.26 Define the function Γ, s- TOYt_ņ2] . În...
Time series question about independent stationary processes
2:23 Two processes |Z, and (Y are said to be independent if for any time points 11 Im and s1.8-2... Sn the random variables [Z, Z,. ..Z, are independent of the random variables [Ys,. Ys, ..., Y). Show that if IZ) and Y are inde- 23 mm pendent stationary proesses, then W-2,+ 7 is stationary.
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...