Question

Suppose a sample of size n follows an AR(1) process with lag 1 autocorrelation rho1​=α. Use Equation (5.5) to find the variance of the sample mean.

Answer 1

The variance of the sample mean in an AR(1) process with lag 1 autocorrelation can be calculated using Equation (5.5).

Step-by-step explanation:

In an autoregressive (AR) process with lag 1 autocorrelation, the variance of the sample mean can be calculated using Equation (5.5):

Variance = (1 - α²)/(n - 1)

Here, n represents the sample size and α represents the lag 1 autocorrelation coefficient (rho1).

For example, if we have a sample of size n = 100 and the lag 1 autocorrelation coefficient is α = 0.8:

Variance = (1 - 0.8²)/(100 - 1) = 0.0084