Nonparametric seasonal cointegration tests

This paper proposes a new family of nonparametric tests to detect the number of cointegrating relations in seasonally integrated time series systems. This testing framework utilizes and extends the results of Variance-Ratio cointegration tests proposed by Nielsen (2010) and seasonal unit root tests proposed by Ero & gbreve;lu et al. (2018). Based on the ratio of the variance-covariance matrices of the seasonally transformed series and their fractional transforms, the proposed method requires neither a parametric regression model estimation nor a semiparametric serial correlation adjustment. Freed from the specification of the nuisance parameters, we observe significant size and power improvements over existing tests. Moreover, our cointegration tests are flexible enough to capture situations where the cointegration rank is different for different seasonal frequencies.