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The Fredholm Approach to Asymptotic Inference on Nonstationary and Noninvertible Time Series Models

Published online by Cambridge University Press:  11 February 2009

Katsuto Tanaka
Katsuto Tanaka
Affiliation:
Hitotsubashi University, Japan
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Abstract

A unified approach which I call the Fredholm approach is suggested for the study of asymptotic behavior of estimators and" test statistics arising from nonstationary and/or noninvertible time series models. Some limit theorems are given concerning the distribution of (the ratio of) quadratic (plus linear) forms in random variables generated by a linear process that is not necessarily stationary. Especially, the limiting characteristic function is derived explicitly via the Fredholm determinant and resolvent of a given kernel. Some examples are also shown to illustrate our methodology.

Type
Articles
Information
Econometric Theory , Volume 6 , Issue 4 , December 1990 , pp. 411 - 432
Copyright
Copyright © Cambridge University Press 1990

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