Consistency of the drift parameter estimator for the discretized\n fractional Ornstein-Uhlenbeck process with Hurst index H\∈(0, frac12)

2015/01/19 by Kęstutis Kubilius, Kubilius, Kestutis, Yuliya Mishura +5
Economics, Econometrics and Finance · Mathematics · #60F15 #60F25 #60G22 #62F10 #62F12 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1501.04471

openalex publication_date 2015/01/19 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We consider Langevin equation involving fractional Brownian motion with Hurst\nindex H\∈(0, frac12). Its solution is the fractional Ornstein-Uhlenbeck\nprocess and with unknown drift parameter \θ. We construct the estimator\nthat is similar in form to maximum likelihood estimator for Langevin equation\nwith standard Brownian motion. Observations are discrete in time. It is assumed\nthat the interval between observations is n^-1, i.e. tends to zero (high\nfrequency data) and the number of observations increases to infinity as n^m\nwith m>1. It is proved that for positive \θ the estimator is strongly\nconsistent for any m>1 and for negative \θ it is consistent when\nm>\(1)/(2H).\n

Related

• Parameter estimation based on discrete observations of fractional\n Ornstein-Uhlenbeck process of the second kind
• Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the Second Kind
• Parameter estimation for fractional Ornstein-Uhlenbeck processes of general Hurst parameter
• On drift parameter estimation for reflected fractional Ornstein-Uhlenbeck processes
• Hypothesis testing of the drift parameter sign for fractional\n Ornstein-Uhlenbeck process