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Continuous Weak Convergence and Stochastic Equicontinuity Results for Integrated Processes with an Application to the Estimation of a Regression Model

Published online by Cambridge University Press:  11 February 2009

Pentti Saikkonen
Pentti Saikkonen
Affiliation:
University of Helsinki
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Abstract

The concepts of continuous and uniform weak convergence and versions of stochastic equicontinuity are discussed in the context of integrated processes of order one. The considered processes depend on a parameter vector in a specific fashion which is relevant for integrated and cointegrated systems with non-linearities in parameters. The results of the paper can be applied to obtain asymptotic distributions of estimators and test statistics in such systems. In a correctly specified cointegrated Gaussian system, this can be done in a very convenient way. Combining the results of this paper with available general maximum likelihood estimation theories readily shows that the maximum likelihood estimator is asymptotically optimal with a mixed normal limiting distribution. The usefulness of this approach is demonstrated by analyzing a regression model with autoregressive moving average errors and strictly exogenous regressors which may be either integrated of order one, asymptotically stationary, or nonstochastic and bounded.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 2 , April 1993 , pp. 155 - 188
Copyright
Copyright © Cambridge University Press 1993

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