Modeling process asymmetries with Laplace moving average

Many records in environmental science exhibit asymmetries: for example in shallow water and with variable bathymetry, the sea wave time series shows front–back asymmetries and different shapes for crests and troughs. In such situation, numerical models are available but their computational cost and complexity are high. A stochastic process aimed at modeling such asymmetries has recently been proposed, the Laplace moving average process, which consists in applying a linear filter on a non-Gaussian noise built using the generalized Laplace distribution. The objective is to propose a new non-parametric estimator for the kernel involved in the definition of this process. Results based on a comprehensive numerical study will be shown in order to evaluate the performances of the proposed method.