Mixture periodic GARCH models: Applications to exchange rate modeling

In this paper, we propose an extension of a mixture periodic ARCH model (MPARCH) to a mixture periodic GARCH model (MPGARCH), and provide some probabilistic properties of this class of models. An estimation method based on the Expectation-Maximization (EM) algorithm is proposed. Finally, it is applied to model the spot rates of the Algerian Dinar against the U.S.-Dollar and Euro. The empirical analysis demonstrates that the proposed mixture model yields the best performance among the competing models.