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.

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doi.org/10.1111/j.1467-9892.1996.tb00274.x, hdl.handle.net/1765/2062
Journal of Time Series Analysis
Erasmus School of Economics

Franses, P. H.& Boswijk, P. (1996). Unit roots in periodic autoregressions. Journal of Time Series Analysis, 221–245.https://doi.org/10.1111/j.1467-9892.1996.tb00274.x