Linearity tests under the null hypothesis of a random walk with drift

摘要

This paper examines the linearity tests against smooth transition autoregressive models under the null hypothesis of a random walk with drift. The results show that the limiting distribution of the Wald-type statistic proposed by Terasvirta (1994) and the statistic proposed by Harvey and Leybourne (2007) follow the standard distribution, whereas the robust statistic proposed by Harvey et al. (2008) diverges at a rate of . The finite sample simulations show is oversized, and the robust test proposed by Harvey and Leybourne (2007) has better power performance despite being slightly undersized. Therefore, the robust statistic is recommended to be used as a conservative test in practical applications.