Asymptotic distribution of the autoregressive estimates of the inverse correlation function (Q1063349)

We consider a one-sided, infinite moving average process, with absolutely summable coefficients, of independent identically distributed random variables, \(\epsilon_ t\), with 0 mean and finite fourth moment. The spectral density of the process is also assumed to be non-vanishing. Using observations \(X_ 1,...,X_ T\) from \(x_ t\), an autoregression of order k, where \(k\to \infty\), \(k^ 3/T\to 0\) as \(T\to \infty\), is assumed to be fitted for estimating the inverse covariance and correlation functions of \(x_ t\). By further assuming that k is asymptotically sufficient to overcome the bias in approximating an infinite order autoregressive process by a process with finite order, the joint asymptotic normality of the estimated inverse covariance and correlation functions is established.