Suppose we are working with a time series X1, X2, X3, X4, X5, and have observed one realiza-

tion of the series x1 =2,x2 =1,x3 =4,x4 =4,x5 =0.

(a) Without assuming that the series is stationary, how can we estimate μt and γ(s, t) (i. e., how can we

estimate the population mean and covariance functions using just one realization)?

(b) Do you think the estimates in (a) are "good"? Explain.

(c) Now assume the series is stationary. How can we estimate μt and γ(s, t)?

(d) Why would you expect the estimates from (c) to be better than those from (a)?

(e) Based on your answers above, explain the importance of stationarity.