Question

Sample mean X = 0:157 was computed from a sample of size 100 generated from a MA(1) process with mean and = 0:6, 2 = 1. Construct an approximate 95% CI for . Are the data compatible with the hypothesis that = 0

Answer 1

Answer:

Step-by-step explanation:

The variance of the sample mean for an MA(1) process and procedure is in general

$Var(X_{n}) = \frac{1}{n}\sum_{h = -n}^{n}(1-\frac{|h|}{n})\sigma _{n} =\frac{1}{n}(\sigma ^{2}(1+\Theta ^{2})+2(1-\frac{1}{n})\sigma ^{2}\Theta )$

Thus, in this case, we have Var(Xn) = 0.00172. An approximate 95% confidence interval for μ is then given by

$\bar{x}_{n}\pm \sqrt{Var(\bar{X}_{n})} = 0.157\pm 1.96\sqrt{0.00172} = 0.157\pm 0.081$

This interval does not involve the value 0, so the data are not compatible with the hypothesis that μ= 0.