Dept. Math, Hokkaido Univ. EPrints Server

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);

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Abstract

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.

Item Type:Preprint
Additional Information:0
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
ID Code:1677