On Asymptotic Distribution of Parameter Free tests for Ergodic Diffusion Processes

TL;DR

This paper develops asymptotically distribution-free goodness of fit tests for ergodic diffusion processes, applicable to both parametric and non-parametric hypotheses, including Ornstein-Uhlenbeck and switching processes.

Contribution

It introduces new asymptotically parameter free tests of Cramér-von Mises type for ergodic diffusion processes, covering both parametric and non-parametric hypotheses.

Findings

Proposes asymptotically distribution free tests for parametric diffusion models.

Extends testing procedures to a wider class of trend coefficients.

Validates tests through theoretical analysis and simulations.

Abstract

We consider two problems of constructing of goodness of fit tests for ergodic diffusion processes. The first one is concerned with a composite basic hypothesis for a parametric class of diffusion processes, which includes the Ornstein-Uhlenbeck and simple switching processes. In this case we propose asymptotically parameter free tests of Cram\'er-von Mises type. The basic hypothesis in the second problem is simple and we propose asymptotically distribution free tests for a wider class of trend coefficients.