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Empirical Economics

Erschienen in:

19.11.2015

The Fourier approximation and testing for the null of cointegration

verfasst von: Ching-Chuan Tsong, Cheng-Feng Lee, Li-Ju Tsai, Te-Chung Hu

Erschienen in: Empirical Economics | Ausgabe 3/2016

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Abstract

In this paper, we propose a test to investigate the null of cointegration allowing for structural breaks of unknown form in deterministic trend by using the Fourier form. The test is developed on the basis of the fact that structural breaks of unknown form can be approximated with a low-frequency Fourier component. As a result, the statistic is able to test cointegration without estimating specific break dates. The asymptotic distribution of the test is derived, and the asymptotic critical values are tabulated. Simulation experiments show that the test can deliver robust type I error for various breaks commonly seen in economic analysis and have good power, even in small sample sizes encountered in empirical studies. Our test is applied to analyze the issue of fiscal sustainability in the nine OECD countries with a high debt-to-GDP ratio.

Vorheriger Artikel Testing for unit roots in nonlinear heterogeneous panels with smoothly changing trends: an application to Scandinavian unemployment rates

Nächster Artikel Asymmetric price transmission within the Argentinean stock market: an asymmetric threshold cointegration approach

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We thank one of the referees for this helpful comment.

The result is obtained under \(L=O(T^{1/3})\) as suggested in Andrews (1991), with L denoting the bandwidth used to estimate the long-run variance of \(v_{1t} \). We set \(L=O(T^{1/3})\) in the proofs throughout this paper.

The results for BIC is quantitatively similar to the counterparts with AIC, and they are omitted for brevity.

We also compare power performances of our test and the Shin’s test when there are no structural breaks. Not surprisingly, the results reveals that the former has a slightly power reduction since two additional parameters associated with the Fourier form are estimated. To conserve space, these results are omitted, and can be obtained from the authors upon request.

Please refer to the website: http://stats.oecd.org/Index.aspx?DataSetCode=EO95_INTERNET.

The results with AIC are similar to the counterparts with BIC, and the only exception is the chosen lead and lag terms. Hence, they are omitted for brevity, and can be obtained from the authors upon request.

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Titel: The Fourier approximation and testing for the null of cointegration
verfasst von: Ching-Chuan Tsong
Cheng-Feng Lee
Li-Ju Tsai
Te-Chung Hu
Publikationsdatum: 19.11.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 3/2016
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-015-1028-6

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