Simultaneous Test of the Regular and Seasonal Unit Roots based on the Durbin-Watson Statistic

Many economic time series often contain both regular and seasonal unit roots. For those time series successive applications of the unit root tests, i.e., regular unit root test after the seasonal unit root test or the seasonal unit root test after the regular unit root test, can not control the level of the tests. In this paper we propose a Durbin-Watson (DW) type test statistic for the simultaneous test of both types of unit roots when the errors are independent. The limiting distributions of the proposed test statistics are the functionals of standard Brownian motions. We also obtain the finite distributions and powers of the test statistics using the Imhof (1961) routine.