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On the maximal entropy property for ARMA processes and ARMA approximation

Published online by Cambridge University Press:  01 July 2016

Dawei Huang
Dawei Huang*
Affiliation:
Peking University
*
∗Present address: School of Mathematics, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia.
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Abstract

The existence and properties of a general ARMA (p, q) process, whose autocovariances, up to lag p, and impulse coefficients, up to lag q, coincide with some given values, are shown. A closed-form solution is obtained. Based on this, the maximal entropy property for ARMA process and the relation and difference between ARMA maximal entropy approximation and extended Padé approximation are discussed. This method may be used for the design of digital filters and for ARMA spectral estimation.

Keywords

MAXIMAL ENTROPY PROPERTYARMA PROCESSARMA APPROXIMATIONZERO LOCATION OF POLYNOMIAL
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 612 - 626
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

This paper was written during the author's visit to the Department of Statistics, Research School of Social Sciences, Australian National University, and was revised in the School of Mathematics, Queensland University of Technology.

References

Anderson, B. D. O. and Skelton, R. E. (1987) The generation of all q-Markov covers. Preprint, Department of Systems Engineering, Australian National University.CrossRefGoogle Scholar
Antoniou, A. (1982) Digital Filters: Analysis and Design. McGraw-Hill, New York.Google Scholar
Doob, J. L. (1944) The elementary Gaussian processes. Ann. Math. Statist. 15, 229–282.CrossRefGoogle Scholar
Franke, J. (1985) ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses. Adv. Appl. Prob. 17, 810–840.CrossRefGoogle Scholar
Glover, K. (1984) All optimal Hankel-norm approximations of linear multivariate systems and their L8 error bounds. Internat. J. Control 39, 1115–1193.CrossRefGoogle Scholar
Hannan, E. J. (1987) Rational transfer function approximation. Statist. Sci. 2, No. 2, 135–161.Google Scholar
Hannan, E. J. and Kavalieris, L. (1984) A method for autoregressive-moving average estimation. Biometrika 71, 281–289.CrossRefGoogle Scholar
Hannan, E. J. and Rissanen, J. (1982) Recursive estimation of mixed autoregressive-moving average order. Biometrika 69, 81–94.CrossRefGoogle Scholar
Hastings-James, R. and Mehra, S. K. (1977) Extensions of the Padé-approximate technique for the design of recursive filters. IEEE Trans. Acoust., Speech, Signal Proc. 25, 501–509.CrossRefGoogle Scholar
Huang, Dawei (1988) Recursive method for ARMA model estimation(I). Acta Math. Appl. Sinica, English Series 4, 169–192.CrossRefGoogle Scholar
Huang, Dawei (1989) Recursive method for ARMA model estimation(II). Acta Math. Appl. Sinica, English Series 5 (4) 332–354.Google Scholar
Kolmogoroff, A. (1941) Stationary sequence in Hilbert space (in Russian). Bull. Math. Univ. Moscou 2, No. 6.Google Scholar