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

10.29973/JCSA.200403.0005

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

Autoregressive ； growth curves model ； MANOVA ； multivariate linear model

中國統計學報

42卷1期（2004 / 03 / 01）

81 - 89

英文

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.

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