Abstract
AbstractIn view of applications to diagnostic tests of ARMA models, the asymptotic behavior of multivariate empirical and copula processes based on residuals of ARMA models is investigated. Multivariate empirical processes based on squared residuals and other functions of the residuals are also investigated. It is shown how these processes can be used to develop distribution free tests of change-point analysis and serial independence. It is also demonstrated that these empirical processes provide an easy mechanism for developing goodness-of-fit tests for the distribution of the innovations, and that the well-known Lilliefors test can be applied to the residuals of ARMA models without any change.KeywordsSequential Empirical ProcessARMA ModelResidual SquaresCopula ProcessSerial IndependenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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