AR and MA representation of partial autocorrelation functions, with applications
Preprint Series # 829
Inoue, Akihiko AR and MA representation of partial autocorrelation functions, with applications. (2007);
We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.
|Uncontrolled Keywords:||Partial autocorrelation functions, Verblunsky coefficients, orthogonal polynomials on the unit circle, Baxter's condition, fractional ARIMA processes, long memory|
|Subjects:||60-xx PROBABILITY THEORY AND STOCHASTIC PROCESSES|