On the optimal forecast with the fractional Brownian motion

• Main Authors: WANG, Xiaohu, ZHANG, Chen, Jun YU
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2022
• Subjects: Fractional Gaussian noise; Conditional expectation; Anti-persistence; Continuous record; Discrete record; Optimal forecast; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2632; https://ink.library.smu.edu.sg/context/soe_research/article/3631/viewcontent/Forecasting_fBm06.pdf
• Institution: Singapore Management University

This paper examines the performance of alternative forecasting formulae with the fractional Brownian motion based on a discrete and finite sample. One formula gives the optimal forecast when a continuous record over the infinite past is available. Another formula gives the optimal forecast when a continuous record over the finite past is available. Alternative discretiza-tion schemes are proposed to approximate these formulae. These alternative discretization schemes are then compared with the conditional expectation of the target variable on the vector of the discrete and finite sample. It is shown that the conditional expectation delivers more accurate forecasts than the discretization-based formulae using both simulated data and daily realized volatility (RV) data. Empirical results based on daily RV indicate that the conditional expectation enhances the already-widely known great performance of fBm in forecasting future RV.