LOCAL ASYMPTOTIC NORMALITY OF MULTIVARIATE ARMA PROCESSES WITH A LINEAR TREND

BERNARD GAREL^{1} AND MARC HALLIN^{2}

1Institut National Polytechnique, ENSEEIHT, 2, rue Camichel, F-31071 Toulouse Cédex, France

2Institut de Statistique, Université Libre de Bruxelles, Campus de la Plaine CP210, Boulevard du Triomphe, B-1050 Bruxelles, Belgium

(Received November 16, 1993; revised October 12, 1994)

Abstract. 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 term. In contrast with earlier univariate results, the central sequence here is correlogram-based, i.e. expressed in terms of a generalized concept of residual cross-covariance function.

Key words and phrases: Multivariate linear model, multivariate ARMA process, local asymptotic normality.