THRESHOLD MODELS FOR LEVY PROCESSES AND APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATION

Abstract

Using the Levy process (the solution to the Ito–Skorokhod stochastic differential equation) we propose the construction of the model of the threshold process and the approximate maximum likelihood method based on approximation of the logarithmic function of the likelihood of observations. The estimates for the parameters of the two-mode threshold jump process with discretely sampled data are found. We show that by checking the likelihood ratio, determining the presence of threshold effects is possible. Keywords: threshold jump process, approximate maximum likelihood method, stochastic differential equation.