Some lagrange multiplier tests for seasonal differencing

Abstract

Determining whether a time series has a unit root is an important problem in many time series analyses. For seasonal time series the problem is more complicated as one has to decide whether both regular and seasonal differencing or just one of them would suffice to transform a series into stationarity. This important problem is addressed via the Lagrange multiplier test approach. The large sample representations of the test statistics in terms of integrals of Wiener processes are obtained. These facilitate the tabulation of the large sample distribution of the statistics. Some empirical results are reported. © 1991 Biometrika Trust.