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Johansen test with Fourier-type smooth nonlinear trends in cointegrating relations

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  • Takamitsu Kurita
  • Mototsugu Shintani

Abstract

We develop a methodology for testing the cointegrating rank in vector autoregressive (VAR) models in the presence of Fourier-type smooth nonlinear deterministic trends in cointegrating relations. The limiting distribution of log-likelihood ratio test statistics is derived, and approximate limit quantiles are tabulated. A sequential procedure to select the cointegrating rank is evaluated by Monte Carlo simulations. Our empirical application to economic data also demonstrates the usefulness of the proposed methodology in a practical context.

Suggested Citation

  • Takamitsu Kurita & Mototsugu Shintani, 2025. "Johansen test with Fourier-type smooth nonlinear trends in cointegrating relations," Econometric Reviews, Taylor & Francis Journals, vol. 44(10), pages 1589-1616, November.
    • Handle: RePEc:taf:emetrv:v:44:y:2025:i:10:p:1589-1616
    DOI: 10.1080/07474938.2025.2530640
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