Publication Type
Working Paper
Version
publishedVersion
Publication Date
10-2022
Abstract
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.
Keywords
Fractional Gaussian noise, Conditional expectation, Anti-persistence, Continuous record, Discrete record, Optimal forecast
Discipline
Econometrics
Research Areas
Econometrics
First Page
1
Last Page
28
Publisher
SMU Economics and Statistics Working Paper Series Paper No. 12-2022
City or Country
Singapore
Citation
WANG, Xiaohu; ZHANG, Chen; and Jun YU.
On the optimal forecast with the fractional Brownian motion. (2022). 1-28.
Available at: https://ink.library.smu.edu.sg/soe_research/2632
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.