Cipra, Tomáš Simple correlated ARMA processes. (English) Zbl 0564.62071 Math. Operationsforsch. Stat., Ser. Stat. 15, 513-524 (1984). 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 Cited in 1 Document MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:bivariate ARMA model; correlation structure; residual correlations; simple correlated ARMA process; autocorrelations; cross correlations; partial autocorrelations; Simultaneous estimation; conditional maximum likelihood; diagnostic checking; model building Citations:Zbl 0438.62071; Zbl 0496.62077 PDFBibTeX XMLCite \textit{T. Cipra}, Math. Operationsforsch. Stat., Ser. Stat. 15, 513--524 (1984; Zbl 0564.62071) Full Text: DOI