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

Alexander Kukush; Yuliya Mishura; Kostiantyn Ralchenko

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arXiv · 1604.02645

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

Alexander Kukush·Yuliya Mishura·Kostiantyn Ralchenko

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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 $H\in(0,1)$.

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Alexander Kukush, Yuliya Mishura, Kostiantyn Ralchenko. 2016-04-10. Hypothesis testing of the drift parameter sign for fractional Ornstein-Uhlenbeck process. https://arxiv.org/abs/1604.02645

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