Maximum Likelihood Estimation of Fractional Ornstein-Uhlenbeck Process with Discretely Sampled Data
Holder： Xiaohu Wang（Fudan University）
Time：2025-03-27 15:10-17:00
Location：Room 217, Guanghua Building 2
Abstract:
This paper first derives two analytic formulae for the autocovariance of the discretely sampled fractional Ornstein-Uhlenbeck (fOU) process. Utilizing the analytic formulae, two main applications are demonstrated: (i) investigation of the accuracy of the likelihood approximation by the Whittle method; (ii) the optimal forecasts with fOU based on discretely sampled data. The finite sample performance of the Whittle method and the derived analytic formula motivate us to introduce a feasible exact maximum likelihood (ML) method to estimate the fOU process. The long-span asymptotic theory of the ML estimator is established, where the convergence rate is a smooth function of the Hurst parameter (i.e., H) and the limiting distribution is always Gaussian, facilitating statistical inference. The asymptotic theory is different from that of some existing estimators studied in the literature, which is discontinuous at H = 3/4 and involves non-standard limiting distributions. The simulation results indicate that the ML method provides more accurate parameter estimates than all the existing methods, and the proposed optimal forecast formula offers a more precise forecast than the existing formula. The fOU process is applied to fit daily realized volatility (RV) and daily trading volume series. When forecasting RVs, it is found that the forecasts generated using the optimal forecast formula with the parameter estimates from the ML method outperform those generated from the combinations of alternative estimation methods and alternative forecast formula.
About the Speaker:
王晓虎，复旦大学经济学院，教授，博士生导师，复旦-安联金融保险研究中心主任。国家级青年人才项目获得者，上海市曙光学者，上海市浦江人才。主要研究方向为金融计量学和金融资产定价，研究成果发表在 Journal of Econometrics, Econometrics Journal, Econometric Reviews, Journal of International Money and Finance, Economic Letters 等国际权威学术期刊上。担任《世界经济文汇》编辑。
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