This paper proposes a new test for the presence of a nonlinear deterministic trend approximated by a Fourier expansion in a univariate time series for which there is no prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. Our approach builds on...

Perron and Yabu (2008) consider the problem of testing for a break occuring at an unknown date in the trend function of a univariate time series when the noise component can be either stationary or integrated. This paper extends their work by proposing a sequential test that allows one to test...

This paper considers the problem of testing for multiple structural changes in the persistence of a univariate time series. We propose sup-Wald tests of the null hypothesis that the process has an autoregressive unit root against the alternative hypothesis that the process alternates between...

Roy, Falk and Fuller (2004) presented a procedure aimed at providing a test for the value of the slope of a trend function that has (nearly) controlled size in autoregressive models whether the noise component is stationary or has a unit root. In this note, we document errors in both their...

This paper considers the problem of testing for structural changes in the trend function of a univariate time series without any prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. We propose a new approach that builds on the work of Perron...

Perron (1989) introduced unit root tests valid when a break at a known date in the trend function of a time series is present, which are invariant to the magnitude of the shift in level and/or slope and to allow them under both the null and alternative hypotheses. The subsequent literature...