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

Takamitsu Kurita and Mototsugu Shintani

Econometric Reviews, 2025, vol. 44, issue 10, 1589-1616

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.

Date: 2025
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DOI: 10.1080/07474938.2025.2530640

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