Explicit representation of finite predictor coefficients and its applications
Preprint Series # 646
Inoue, Akihiko and Kasahara, Yukio Explicit representation of finite predictor coefficients and its applications. (2004);
We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof involves the alternate iteration of projection operators associated with the infinite past and the infinite future. We provide several applications, which include rates of convergence of the finite predictor coefficients, an equality of Baxter-type for long memory processes, and a simple representation of the partial autocorrelation function (PACF). We use the last result to obtain the precise asymptotic behavior of PACF with remainder, for the fractional ARIMA processes.
|Uncontrolled Keywords:||Predictior coefficients, AR coefficients, MA coefficients,
prediction, fractional ARIMA processes, long memory, Baxter's inequality, partial autocorrelation functions|
|Subjects:||60-xx PROBABILITY THEORY AND STOCHASTIC PROCESSES|