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

Katsuto Tanaka

Econometric Theory, 1990, vol. 6, issue 04, pages 411-432

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.

Date: 1990

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