On the use of integer and fractional flexible Fourier form Dickey-Fuller unit root tests

Abstract: In this paper we propose the use of a new set of conservative critical values for the flexible Fourier form Dickey-Fuller unit root test when the Fourier frequency is estimated. We consider both the integer frequency and the fractional frequency version of the test and investigate their size and power properties. We find that the integer frequency test sometimes has zero power when the deterministic component of the data generating process is characterized by a fractional frequency. Furthermore, when the originally proposed critical values are applied both versions of the test are oversized when the frequency is estimated. However, whereas the integer frequency test is only moderately oversized the fractional frequency test is significantly oversized in many cases. To remedy the size problems we simulate new critical values for the case where the frequency is estimated. The critical values are conservative, and hence yields an undersized test in some cases. Nevertheless, the resulting fractional frequency test with the new conservative critical values applied to it has good power properties.