On time series with randomized unit root and randomized seasonal unit root

Abstract

A time series model with possibly a randomized unit root and a randomized seasonal unit root is considered. Two statistical tests are developed for the null hypothesis of fixed unit roots against the alternative that the roots are random and fluctuate about the value of one. The testing problem is addressed via the score test approach. The asymptotic representations of the test statistics in terms of Brownian processes are obtained. Simulations are used to tabulate finite sample critical values and to investigate empirical sizes and powers. A Markov chain Monte Carlo approach is proposed for the estimation of model parameters. Both randomized unit root and randomized seasonal unit root are demonstrated to be present in a US money supply data.