The Hurst exponent is a measure of the long-term memory of time series data. It quantifies the relative tendency of a time series either to regress strongly to the mean or to cluster in a direction.

Usage in Statistics

In statistics, the Hurst exponent is used to analyze the randomness and predictability of time series data. A value of H ranges between 0 and 1 and indicates the following:

• H = 0.5: The time series is a random walk. It has no correlation, and past movements do not influence future movements.
• 0 < H < 0.5: The time series exhibits mean reversion. The series tends to return to its long-term mean, and its increments are negatively correlated.
• 0.5 < H < 1: The time series shows long-term positive correlation. Past movements influence future movements in the same direction, indicating persistence.

Application in Trading

In trading, the Hurst exponent is used to identify market trends and the predictability of price movements. Traders use the Hurst exponent to make more informed decisions by understanding the market's behavior:

• H < 0.5: Indicates a mean-reverting market, suggesting that prices will likely return to an average level over time. This can guide strategies like range trading.
• H = 0.5: Suggests a random market where prices follow a random walk. Predictive trading strategies may be less effective in this environment.
• H > 0.5: Implies a trending market, where prices have a higher likelihood of continuing in the same direction. Trend-following strategies can be beneficial here.