On Identification of the Threshold Diffusion Processes

TL;DR

This paper investigates parameter estimation in threshold ergodic diffusion processes, which are continuous-time analogs of threshold autoregressive models, focusing on asymptotic properties and testing hypotheses.

Contribution

It analyzes the asymptotic behavior of maximum likelihood and Bayesian estimators for threshold diffusion models, addressing singular estimation challenges.

Findings

Asymptotic behavior of estimators studied

Rate of convergence is T, not √T

Discusses goodness of fit testing methods

Abstract

We consider the problems of parameter estimation for several models of threshold ergodic diffusion processes in the asymptotics of large samples. These models are the direct continuous time analogues of the well-known in time series analysis threshold autoregressive (TAR) models. In such models the trend is switching when the observed process atteints some (unknown) values and the problem is to estimate it or to test some hypotheses concerning these values. The related statistical problems correspond to the singular estimation or testing, for example, the rate of convergence of estimators is $T$ and not $\sqrt{T}$ as in regular estimation problems. We study the asymptotic behavior of the maximum likelihood and bayesian estimators and discuss the possibility of the construction of the goodness of fit test for such models of observation.