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Local asymptotic normality of multivariate ARMA processes with a linear trend. (English) Zbl 0841.62076

Summary: The local asymptotic normality (LAN) property is established for multivariate ARMA models with a linear trend or, equivalently, for multivariate general linear models with ARMA error terms. In contrast to earlier univariate results, the central sequence here is correlogram-based, i.e. expressed in terms of a generalized concept of residual cross-covariance function.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
62H10 Multivariate distribution of statistics
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