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Two step estimators of the minimum distance type for parameters of the ARMA $(1,1)$ model

I. G. Èrlikh

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A new type of minimum distance estimate is constructed in this paper based on a preliminary estimate. We establish the asymptotic normality of the estimate using a uniform linear expansion of a randomly weighted residual empirical process. Such an expansion is valid in a non-standard neighborhood of the true parameter value. We also discuss asymptotic efficiency of the proposed estimate.

Key words: ARMA model, minimum distance estimates, empirical process, uniform linear expansion.

UDC: 519.233.2+519.246.8

Received: 09.10.2009

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