Hi Please tell that how in Q1 part ix) of R paper the theoritical mean of ACF2MA=0 and theoritical mean of ACF2AR 0.45^2.And how have the asymptotic variance for both ACF2MA and ACF2AR have been calculated? I dont remember reading any formula in the core reading about calculating the mean and variance of ACF of a MA and AR process. Thank you!
Hello The asymptotic distribution for the estimators of auto-correlations of an MA process for lags larger than than order of the process is given on page 24 of Chapter 14. So you need to apply this in the case when k = 2 for this MA(1) model. For the AR process, the asymptotic variance of \( \tilde{\rho}_2 \) is not calculated, only the asymptotic mean. As it is a consistent estimator, this is the true value, ie \( \rho_2 \). Hope this helps Andy
Hi Sindy It is not the mean of the process that we calculate here, rather the asymptotic mean of \( \tilde{\rho}_2 \), the estimator of \( \rho_2 \) for the AR(1) process. This is just \( \rho_2 \) itself, so we need to work out the autocorrelation at lag 2 for the AR(1) process. Hope this helps Andy
