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The Fourier approximation and testing for the null of cointegration

Author

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  • Ching-Chuan Tsong

    (National Chi Nan University)

  • Cheng-Feng Lee

    (National Kaohsiung University of Applied Sciences)

  • Li-Ju Tsai

    (Fu Jen Catholic University)

  • Te-Chung Hu

    (National Kaohsiung University of Applied Sciences)

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.

Suggested Citation

  • Ching-Chuan Tsong & Cheng-Feng Lee & Li-Ju Tsai & Te-Chung Hu, 2016. "The Fourier approximation and testing for the null of cointegration," Empirical Economics, Springer, vol. 51(3), pages 1085-1113, November.
    • Handle: RePEc:spr:empeco:v:51:y:2016:i:3:d:10.1007_s00181-015-1028-6
    DOI: 10.1007/s00181-015-1028-6
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    More about this item

    Keywords

    Cointegration; Fourier approximation; Structural change; Fiscal sustainability;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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