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

Explanation:

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

`Var(X_(n)) = (1)/(n)\sum_(h = -n)^(n)(1-(|h|)/(n))\sigma _(n) =(1)/(n)(\sigma ^(2)(1+\Theta ^(2))+2(1-(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√(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.