A Mixed Asymmetric Laplace Moving Average Process

Abstract

In this paper, we define and study a first order moving average model with Laplace marginal distributions. Extensions to higher orders are discussed. A first order moving average process with mixed Laplace distributions as marginal is developed and studied. The model helps us to simulate mixed Laplace distribution with negative weights. We also introduce a first order moving average process as the mixture of asymmetric Laplace marginals.