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

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  • Tanaka, Katsuto

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.

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  • Tanaka, Katsuto, 1990. "The Fredholm Approach to Asymptotic Inference on Nonstationary and Noninvertible Time Series Models," Econometric Theory, Cambridge University Press, vol. 6(4), pages 411-432, December.
    • Handle: RePEc:cup:etheor:v:6:y:1990:i:04:p:411-432_00
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    Cited by:

    1. Marmol, Francesc, 1996. "Correlation theory of spuriously related higher order integrated processes," Economics Letters, Elsevier, vol. 50(2), pages 169-173, February.
    2. Choi, In & Chul Ahn, Byung, 1998. "Testing the null of stationarity for multiple time series," Journal of Econometrics, Elsevier, vol. 88(1), pages 41-77, November.
    3. Tanaka, Katsuto, 1990. "Asymptotic Distribution of the Least Squares Estimator of the Cointegrating Vector," Economic Review, Hitotsubashi University, vol. 41(3), pages 193-200, July.
    4. Manuel Landajo & María Presno, 2013. "Nonparametric pseudo-Lagrange multiplier stationarity testing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 125-147, February.
    5. Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
    6. Manuel Landajo & María José Presno, 2010. "Stationarity testing under nonlinear models. Some asymptotic results," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 392-405, September.

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