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Title: Testing for a stochastic unit root-type process using Chebyshev time polynomials approximation Authors:  Julio Angel Afonso-Rodriguez - University of the Balearic Islands (Spain) [presenting]
Abstract: Many macroeconomic and financial time series seem to be well characterized by some periods of stationary or nonstationary behaviour, combined with some other periods of explosiveness or exuberance which resembles the bubble phenomenon. Among the different existing possibilities to account for this variety of behaviours, we focus on the case of a stochastic unit root (STUR) type of processes, which includes the pure STUR, the bilinear unit root (BLUR) and the threshold autoregressive STUR (TARSUR) processes. Our main interest is on testing for the existence of this type of processes as the alternative hypothesis to the null of a fixed unit root process. To that end we propose the novelty approach based on introducing a number of trigonometric terms, given by Chebyshev time-polynomials, in the auxiliary regression of the testing procedure to capture the time-varying property of the autoregressive unit root component. We obtain the limiting null and the local-to-the alternative distribution of a generalized pseudo-F ratio test statistic, which have several appealing properties over existing test statistics particularly under serially correlated error terms, and show that it has good power behaviour against any of the particular forms of the STUR-type alternative.