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4. Suppose that in a sample of size 100 from an MA(1) process with mean ????, ???? = -0.6, and ????^2 = 1, we obtain ????100 = 0.157. Construct an approximate 95% confidence interval for ????. Are the data compatible with the hypothesis that ???? = 0? Help: (i) Here ????^2 ? ????_Z^2 is the variance of noise Z_t. (ii) Large sample distribution of X?_n is given as follows: For n large, distribution of the sample mean X?_n is approximately normal with mean ???? ? EX_t and variance n^-1v, where v = ????_X(0) + 2 ?_{1 ? h < n} (1 - h/n)????_X(h). (iii) The autocovariance function ????_X(h) of the MA(1) was calculated in relevant notes

          4. Suppose that in a sample of size 100 from an MA(1) process with mean ????, ???? = -0.6, and ????^2 = 1, we obtain ????100 = 0.157. Construct an approximate 95% confidence interval for ????. Are the data compatible with the hypothesis that ???? = 0?
Help: (i) Here ????^2 ? ????_Z^2 is the variance of noise Z_t.
(ii) Large sample distribution of X?_n is given as follows:
For n large, distribution of the sample mean X?_n is approximately normal with mean ???? ? EX_t and variance n^-1v, where
v = ????_X(0) + 2 ?_{1 ? h < n} (1 - h/n)????_X(h).
(iii) The autocovariance function ????_X(h) of the MA(1) was calculated in relevant notes

4. Suppose that in a sample of size 100 from an MA(1) process with mean ????, ???? = -0.6, and ????^2 = 1, we obtain ????100 = 0.157. Construct an approximate 95% confidence interval for ????. Are the data compatible with the hypothesis that ???? = 0?
Help: (i) Here ????^2 ? ????Z^2 is the variance of noise Zt.
(ii) Large sample distribution of X?n is given as follows:
For n large, distribution of the sample mean X?n is approximately normal with mean ???? ? EXt and variance n^-1v, where
v = ????X(0) + 2 ?1 ? h < n (1 - h/n)????X(h).
(iii) The autocovariance function ????X(h) of the MA(1) was calculated in relevant notes

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