On the Optimal Forecast with the Fractional Brownian Motion

Xiaohu Wang (), Jun Yu and Chen Zhang ()
Additional contact information
Xiaohu Wang: Fudan University
Chen Zhang: Singapore Management University

No 12-2022, Economics and Statistics Working Papers from Singapore Management University, School of Economics

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

Keywords: Fractional Gaussian noise; Conditional expectation; Anti-persistence; Continuous record; Discrete record; Optimal forecast (search for similar items in EconPapers)
JEL-codes: C12 C22 G01 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2022-10-28
New Economics Papers: this item is included in nep-ets, nep-for and nep-sea
References: Add references at CitEc
Citations:

Downloads: (external link)
https://ink.library.smu.edu.sg/soe_research/2632/ Full text (text/html)

Related works:
Journal Article: On the optimal forecast with the fractional Brownian motion (2024)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ris:smuesw:2022_012

Access Statistics for this paper

More papers in Economics and Statistics Working Papers from Singapore Management University, School of Economics 90 Stamford Road, Sigapore 178903. Contact information at EDIRC.
Bibliographic data for series maintained by Cheong Pei Qi ( this e-mail address is bad, please contact ).