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Biometrika 1982 69(1):81-94; doi:10.1093/biomet/69.1.81
© 1982 by Biometrika Trust
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Recursive estimation of mixed autoregressive-moving average order

E. J. HANNAN and J. RISSANEN

Department of Statistics, Australian National University Canberra

The order, (p, q), of an autoregressive-moving average sequence, y(t), may be estimated by minimizing a criterion, log with respect to p and q, where is the maximum likelihood estimate of the variance of the innovations, {varepsilon}(t). It is suggested that, instead, be estimated from a series of regressions of y(t) on where the (t) are obtained by fitting a long autoregression to the data. It is shown how the sequence of regressions may, for p = q, be economically recursively calculated by embedding them in a sequence of bivariate autoregressions. Asymptotic properties of the procedure are established under very general conditions.

Key Words: Autoregressive-moving average • Best coding • Martingale • Recursive calculation • Strong convergence • Vector autoregression


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