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On the Optimal Forecast with the Fractional Brownian Motion

Author

Listed:
  • Wang, Xiaohu

    (Fudan University)

  • Yu, Jun

    (Singapore Management University)

  • Zhang, Chen

    (Singapore Management University)

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.

Suggested Citation

  • Wang, Xiaohu & Yu, Jun & Zhang, Chen, 2022. "On the Optimal Forecast with the Fractional Brownian Motion," Economics and Statistics Working Papers 12-2022, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2022_012
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    Keywords

    Fractional Gaussian noise; Conditional expectation; Anti-persistence; Continuous record; Discrete record; Optimal forecast;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G01 - Financial Economics - - General - - - Financial Crises

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