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

Included in

Econometrics Commons

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