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Simple correlated ARMA processes. (English) Zbl 0564.62071

Let \(\{x_ t\}\) and \(\{y_ t\}\) be ARMA (autoregressive-moving average) processes, defined in terms of operators acting respectively on processes \(a_ t\) and \(b_ t\) such that \((a_ t,b_ t)\) is bivariate normal with means 0, variances \(\sigma^ 2_ a\) and \(\sigma^ 2_ b\), and correlation \(\rho\). Then the bivariate process \(\{(x_ t,y_ t)\}\) is called a simple correlated ARMA process. Following F. Risager’s [Scand. J. Stat., Theory Appl. 7, 49-60 (1980; Zbl 0438.62071) and ibid. 8, 137-153 (1981; Zbl 0496.62077)] analysis of simple correlated autoregressive processes, the present author treats the following for the ARMA case:
a) Results about the autocorrelations, cross correlations and partial autocorrelations; b) Simultaneous estimation by conditional maximum likelihood; c) Verification, that is, diagnostic checking. A final section gives suggestions for a practical approach to model building for this case.
Reviewer: R.Mentz

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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