摘要
This paper establishes probabilistic and statistical properties of the extension of timeinvariant coefficients asymmetric log GARCH processes to periodically time-varying coefficients(P logGARCH)one.In thesemodels,the parameters of log−volatility are allowed to switch periodically between different seasons.The main motivations of this newmodel are able to capture the asymmetry and hence leverage effect,in addition,the volatility coefficients are not a subject to positivity constraints.So,some probabilistic properties of asymmetric P log GARCH models have been obtained,especially,sufficient conditions ensuring the existence of stationary,causal,ergodic(in periodic sense)solution and moments properties are given.Furthermore,we establish the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator(QMLE)under extremely strong assumptions.Finally,we carry out a simulation study of the performance of the QML and the P log GARCH is applied to model the crude oil prices of Algerian Saharan Blend.
