Abstract. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model.

Additional Metadata
Keywords autoregressive time series, unit roots
Persistent URL dx.doi.org/10.1111/j.1467-9892.1996.tb00274.x, hdl.handle.net/1765/2062
Journal Journal of Time Series Analysis
Franses, Ph.H.B.F, & Boswijk, H.P. (1996). Unit roots in periodic autoregressions. Journal of Time Series Analysis, 221–245. doi:10.1111/j.1467-9892.1996.tb00274.x