On the Inverse of the Autocorrelation Matrix for an AR(p) Process

Jack C. Lee ； Ren-Sheng Wang ； Tsung-I Lin

《中國統計學報》 42卷1期 (2004/03) Pp. 81-89

https://doi.org/10.29973/JCSA.200403.0005

並列摘要

Let CN = ( ρ |t-s|), t, s = 1, . . . , N, be the autocorrelation matrix of a vector XN = ( X1, . . . , XN)’ from a stationary autoregressive process of order p, where N ≥ p. In this paper, we derive a general formula without any distributional assumption, which is easy to program for directly solving the inverse of CN, denoted by C . The formulation of C is useful in time series analysis, general linear mode, multivariate linear model, MANOVA and growth curves model with high order autoregressive errors, and can simplify the computational procedure of parameter estimation. Some demonstrations of C including AR(2), AR(3), and AR(4) are given.

並列關鍵字

Autoregressive ； growth curves model ； MANOVA ； multivariate linear model

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