Forecasting Fractional Brownian Motion for Trading Decisions

Summary

The document explains how fractional Brownian motion (fBm), whose non-overlapping increments can be dependent, may support forecasts of future price changes. If log-prices follow this process, its non-Markovian structure can provide information for statistical arbitrage. The work derives theoretical trading-oriented accuracy measures, including hit ratio, expected gain, and risk, rather than assessing forecasts only by conventional statistical criteria.

It also considers practical strategy choices: which past increments to use and when a small predicted move is too uncertain or unprofitable to trade. Empirical applications use high-frequency foreign-exchange rates and realized-volatility series, connecting the forecast analysis with rough volatility. The document’s description does not report specific performance figures, transaction-cost assumptions, or tests beyond those applications, so it does not establish that fBm-based signals will remain profitable in live markets.

Key ideas

• Fractional Brownian motion allows dependence between increments and can make future states forecastable.
• The proposed analysis connects forecast accuracy to hit ratio, expected gain, and strategy risk.
• The choice of lagged increments is a practical input-selection question.
• A no-trade threshold for small predicted increments can affect strategy profitability.
• Applications examine high-frequency FX rates and realized volatility.

Tags

# Forecasting with fractional Brownian motion: a financial perspective


# Forecasting with fractional Brownian motion: a financial perspective









The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the non-Markovian nature of the fBm to forecast future states of the process and make statistical arbitrages. We provide new insights into forecasting an fBm, by proposing theoretical formulas for accuracy metrics relevant to a systematic trader, from the hit ratio to the expected gain and risk of a simple strategy. In addition, we answer some key questions about optimizing trading strategies in the fBm framework: Which lagged increments of the fBm, observed in discrete time, are to be considered? If the predicted increment is close to zero, up to which threshold is it more profitable not to invest? We also propose empirical applications on high-frequency FX rates, as well as on realized volatility series, exploring the rough volatility concept in a forecasting perspective.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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