Title: On Brownian motion approximation of compound Poisson processes with applications to threshold models
Authors: Dong Li - Tsinghua University (China) [presenting]
Abstract: Compound Poisson processes (CPP) constitute a fundamental class of stochastic processes and a basic building block for more complex jump-diffusion processes such as the Levy processes. However, unlike those of a Brownian motion (BM), distributions of functionals, e.g. maxima, passage time, argmin and others, of a CPP are often intractable. We propose a novel approximation of a CPP by a BM so as to facilitate closed-form expressions in concrete cases. Specifically, we approximate, in some sense, a sequence of two-sided CPPs by a two-sided BM with drift, when the threshold effects (e.g. the differences between the regression slopes in two-regime regression) are small but fixed. As applications, we use our approximation to perform statistical inference of threshold models, such as the construction of confidence intervals of threshold parameters. These models include threshold regression (also called two-phase regression or segmentation) and numerous threshold time series models. We conduct numerical simulations to assess the performance of the proposed approximation. We illustrate the use of our approach with a real data set.