Estimation for Stochastic Models Driven by Laplace Motion

Laplace motion is a Lévy process built upon Laplace distributions. Non Gaussian stochastic fields that are integrals with respect to this process are considered and methods for their model fitting are discussed. The proposed procedures allow for inference about the parameters of the underlying Laplace distributions. A fit of dependence structure is also addressed. The importance of a convenient parameterization that admits natural and consistent estimation for this class of models is emphasized. Several parameterizations are introduced and their advantages over one another discussed. The proposed estimation method targets the standard characteristics: mean, variance, skewness and kurtosis. Their sample equivalents are matched in the closest possible way as allowed by natural constraints within this class. A simulation study and an example of potential applications conclude the article.