Recursive identification for multidimensional ARMA processes with increasing variances

In time series analysis, almost all existing results are derived for the case where the driven noise {wn} 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(‖wn‖β| Fn-1), β＞ 2 Is possible to grow up at a rate of a power of logn. The wellknown 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.