Answer Happy

QUESTION 2 [12] Suppose a time series of size follows x, = 4+z, -2- process, wherez, - WN(4,1), 1, k = 0 20, k = 0 1 X, = 0.157, N = -02, k = 1 and Px = k = 1 2 0 otherwise 0 otherwise (4) (4) (a) Calculate the variance of the estimated mean for{x}. (b) Construct an approximate 99% confidence interval for u. (c) Are the data computable with the hypothesis that u=0? (d) Justify your answer in part (c). (2) (2)
QUESTION 1 [18] Table 1 gives a summary of sample autocovariance and autocorrelation functions. Table 1 1 1 2 3 4 5 x, 0 1 2 2 0 î 0 2 0 ..... Ô, 0 1 0 (a) Calculate the missing values of sample autocovariance and autocorrelation functions in Table 1. (8) (b) Calculate 0,2 and 32- (4) (c) If Table 1 was taken from a time series of N = 100 with estimated autocorrelation functions, show whether a time series model is white noise or not. (4) (d) Justify your answer in part (c). (2) QUESTION 2 [12] Suppose a time series of size 50 follows x, = 1 + 2, -2- process, where z, - ~ WN(0,1), 1, k = 0 202, k = 0 1 # = 0.157, 1x = -0, k = 1 and P = {- k = 1 2 0 otherwise 10 otherwise (4) (4) (a) Calculate the variance of the estimated mean for {x,}. (b) Construct an approximate 99% confidence interval for u. (c) Are the data computable with the hypothesis that u = 0? (d) Justify your answer in part (c). (2) (2)