On testing for a stochastic unit root in financial time seriesThe case of a bilinear unit root process

Resumen

This paper considers a particular member of the class of stochastic (or randomized) unit root (STUR) process given by a simple bilinear process with a unit root. Under a certain reparameterization of the bilinear parameter, we use the recently proposed stochastic limit for this process to show the consistency of some commonly used nonparametric tests of the null hypothesis of stationarity against the alternative of a unit root under this form of nonstationarity, other than difference stationarity. Also, as an alternative to the existing pseudo T-ratio test for the null of a fixed unit root against a bilinear unit root, we propose a new testing procedure based on a simple modification of the KPSS test statistic that has the advantage to allow for more general forms of the deterministic component and that seems to have good size and power in finite samples to discriminate between a fixed (or linear) and a bilinear unit root. We derive the asymptotic null and alternative distributions and also we present an application to the series of log-prices of some stock market indexes with distinct time frequencies: IBEX 35, SP500, and Dow Jones Composite Average (daily), and CAC40 (weekly).