Publication Type

Journal Article

Version

submittedVersion

Publication Date

1-2024

Abstract

This paper investigates the performance of different forecasting formulas with fractional Brownian motion based on discrete and finite samples. Existing literature presents two formulas for generating optimal forecasts when continuous records are available. One formula relies on a history over an infinite past, while the other is designed for a record limited to a finite past. In reality, only observations at discrete time points over a finite past are available. In this case, the forecasting formula, which has been widely used in the literature, is the one obtained by Gatheral et al. (2018) that truncates and discretizes the formula based on continuous records over an infinite past. The present paper advocates an alternative forecasting formula, which is the condition expectation based on finite past discrete-time observations. The findings suggest that the conditional expectation approach produces more accurate forecasts than the existing method, as demonstrated by both simulated data and actual daily realized volatility (RV) observations. Moreover, we also provide empirical evidence showing that the conditional expectation approach can lead to larger economic values than the existing method.

Keywords

Fractional Brownian motion, Conditional expectation, Optimal forecast

Discipline

Econometrics

Research Areas

Econometrics

Publication

Quantitative Finance

Volume

24

Issue

2

First Page

337

Last Page

346

ISSN

1469-7688

Identifier

10.1080/14697688.2023.2297730

Publisher

Taylor and Francis Group

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1080/14697688.2023.2297730

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