Hypothesis testing of the drift parameter sign for fractional Ornstein-Uhlenbeck process

TL;DR

This paper introduces a new hypothesis test for the sign of the drift parameter in the fractional Ornstein-Uhlenbeck process, applicable for all Hurst parameters, and proves the consistency of the test and estimators.

Contribution

It presents a novel, universally applicable method for testing the drift sign and establishes the strong consistency of estimators for all Hurst parameters.

Findings

The proposed test is consistent for all H in (0,1).

Estimators for the drift parameter are strongly consistent across all H.

The method extends previous approaches to all Hurst parameters.

Abstract

We consider the fractional Ornstein-Uhlenbeck process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary to the previous works, our approach is applicable for all $H\in(0,1)$. We also study the estimators for drift parameter for continuous and discrete observations and prove their strong consistency for all $H\in(0,1)$.