On periodic EGARCH models. Issue 7 (3rd July 2022) - Sadoun, Mohamed; Bentarzi, Mohamed
Abstract: This article deals with some probabilistic and statistical properties of a periodic exponential GARCH ( 1, 1 ) model, which is very adequate and appropriate to capture and describe, at the same time, three stylized facts very often encountered in the field of financial time series namely, the volatility clustering, the asymmetry and the periodicity exhibited by the autocovariance structure. Indeed, necessary and sufficient conditions for the periodical stationarity, both in second order and strict, are established. The closed form of the second-order moment is, under these conditions, established. Moreover, the higher order moments structure is studied. The conditional least square (CLS) and the quasi maximum likelihood estimations of the PEGARCH M ( 1, 1 ) model are obtained. Moreover, the CLS estimations of the non-centered PEGARCH M ( 1, 1 ) model and the PAR M ( 1 ) − PEGARCH M ( 1, 1 ) are established. The performances of these estimators were assisted by an intensive simulation study, moreover an application on real data set is provided.