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Recursive identification for multidimensional ARMA processes with increasing variances

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Abstract

In time series analysis, almost all existing results are derived for the case where the driven noise {w n } in the MA part is with bounded variance (or conditional variance). In contrast to this, the paper discusses how to identify coefficients in a multidimensional ARMA process with fixed orders, but in its MA part the conditional moment \(E(\parallel w_n \parallel ^\beta |\mathcal{F}_n - 1),\beta > 2\) is possible to grow up at a rate of a power of log n. The well-known stochastic gradient (SG) algorithm is applied to estimating the matrix coefficients of the ARMA process, and the reasonable conditions are given to guarantee the estimate to be strongly consistent.

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Authors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080, Beijing, China

    Chen Hanfu

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  1. Chen Hanfu
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Chen, H. Recursive identification for multidimensional ARMA processes with increasing variances. Sci China Ser F 48, 596–614 (2005). https://doi.org/10.1360/04yf0324

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  • DOI: https://doi.org/10.1360/04yf0324

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