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Asymptotic properties of time domain gaussian estimators

Published online by Cambridge University Press:  01 July 2016

R. Kohn
R. Kohn*
Affiliation:
The Australian National University, Canberra
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Abstract

We consider a general non-linear multivariate time series model which can be parameterized by a finite and fixed number of parameters and which can be rewritten, if necessary, in a form such that the disturbances are stationary martingale differences. Given a series of discrete, equally spaced observations we prove the strong consistency and asymptotic normality of the Gaussian estimators of the parameters, the parameters possibly being subject to non-linear constraints. Because the normal equations are usually highly non-linear it may be difficult to obtain explicit expressions for the Gaussian estimates. To overcome this problem we use a Gauss–Newton type algorithm to obtain a sequence of iterates which converge to, and have the same asymptotic properties as, the Gaussian estimates.

Keywords

CENTRAL LIMIT THEOREMCONSTRAINTSGAUSS-NEWTONGAUSSIAN ESTIMATESMARTINGALE DIFFERENCESMULTIVARIATE TIME SERIESNON-LINEAR

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 2 , June 1978, pp. 339 - 359
Copyright
Copyright © Applied Probability Trust 1978 

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