Testing for unit roots in bounded time series.
(with G. Cavailiere)
Many key economic and financial series are bounded, in the sense that they have bounds either below, or above, or both. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we fill this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We propose new augmented Dickey-Fuller type tests as well as new versions of the modified M tests developed by Ng and Perron (2001) and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. Numerical evidence suggests that the proposed tests perform remarkably well in finite samples for a range of limited processes. Moreover, the proposed tests outperform the Phillips-Perron type tests originally proposed in Cavaliere (2005). An empirical illustration using U.S. interest rate data concludes.