On Periodic Autogressive Conditional Heteroskedasticity

Asset returns exhibit clustering of volatility throughout the year. This paper proposes a class of models featuring periodicity in conditional heteroskedasticity. The periodic structures in GARCH models share many properties with periodic ARMA processes studied by Gladyshev (1961), Tiao and Grupe (1980) and others. We describe the relation between periodic GARCH processes and time-invariant (seasonal) GARCH processes. Besides the periodic GARCH or P-GARCH process, we also discuss P-IGARCH, PI-GARCH, P-ARCH-M and P-EGARCH processes. Extensions to multivariate ARCH processes are studied as well. Moreover, we also consider periodicity in the common persistence of volatility for several series. A quasi-maximum likelihood estimator following Bollerslev and Wooldridge (1992) is defined and a LM test for periodicity derived from it. The models are applied to several asset pricing series.
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