Some Aspects of Asymptotic Theory with Applications to Time Series Models

P. Jeganathan

Econometric Theory, 1995, vol. 11, issue 05, pages 818-887

Abstract: The primary purpose of this paper is to review a very few results on some basic elements of large sample theory in a restricted structural framework, as described in detail in the recent book by LeCam and Yang (1990, Asymptotics in Statistics: Some Basic Concepts. New York: Springer), and to illustrate how the asymptotic inference problems associated with a wide variety of time series regression models fit into such a structural framework. The models illustrated include many linear time series models, including cointegrated models and autoregressive models with unit roots that are of wide current interest. The general treatment also includes nonlinear models, including what have become known as ARCH models. The possibility of replacing the density of the error variables of such models by an estimate of it (adaptive estimation) based on the observations is also considered.

Date: 1995
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