On Periodic Structures and Testing for Seasonal Unit Roots

A Bayesian analysis of periodic integration

“…Simulation results in Franses (1996b) and Ooms and Franses (1996) among others show that, when one neglects periodic parameter variation in the periodically integrated autoregressions (PIAR), one may or may not ®nd seasonal unit roots and may face under-or overadjustment of the`adjusted' time series. Furthermore, the recent results in Ghysels, Hall, and Lee (1996) and Boswijk, Franses, and Haldrup (1996) show that once one allows for periodicity any evidence for seasonal unit roots tends to disappear. To summarize, the empirical results in Franses and Paap (1994) and Franses (1996b) suggest rather strong empirical evidence of periodic integration in many univariate macroeconomic time series.…”

Asymmetry and nonstationarity for a seasonal time series model

“…Note that there are many versions of threshold time series models such as TAR models with indicator of the form I 1t ¼ Iðy tÀq XlÞ, momentum TAR (MTAR) models with indicator of the form I 1t ¼ Iðy tÀ1 À y tÀqÀ1 XlÞ, and multiple regime extensions of them. Also, seasonal nonstationarity is discussed in different models such as the DHF model of seasonal autoregression, the HEGY model characterized by the regressors (2.5), and the periodic autoregression of Ghysels et al (1996) and Boswijk and Franses (1996). A threshold DHF model was investigated by Shin and Lee (2003) in the title of seasonal unit root tests and symmetry tests for MTAR models, which can be straightforwardly extended to TAR models if I 1t ¼ Iðy tÀ1 À y tÀqÀ1 XlÞ is replaced by I 1t ¼ Iðy tÀq XlÞ.…”

Adaptive Estimation of Causal Periodic Autoregressive Model

“…The considerable interest given to the class of linear and nonlinear periodic models is explained by its usefulness and appropriateness for modeling stationary periodically correlated processes (Gladyshev, 1961), which are very often met in many fields particularly in economics (e.g., Ghysels et al, 1996;Osborn and Smith, 1989; and others) as well as in hydrology and environmental studies (Bloomfield et al, 1994;Salas et al, 1982;Ula and Smadi, 1997;Vecchia et al, 1983;others).…”