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Filtered Likelihood for Point Processes

by Kay Giesecke of the Stanford University, and
Gustavo Schwenkler of the Stanford University

July 28, 2011

Abstract: We develop likelihood estimators of the parameters of a point process and of incompletely observed explanatory factors that influence the arrival intensity along with the point process itself. The factors follow jump-diffusions whose drift, diffusion and jump coefficients are allowed to depend on the point process. They may be observed completely, at a collection of dates, or not at all. We provide conditions guaranteeing consistency and asymptotic normality. We also establish an approximation scheme for the likelihood, and analyze the convergence and asymptotic properties of the associated estimators. Numerical results illustrate our approach.

AMS Classification: 62F12, 62M20, 62N02.

Keywords: point process, ltering, parametric maximum likelihood, asymptotic theory, likelihood approximation

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