Detecting patterns in a time series using the Hurst exponent
In finance, a lot of trading strategies are based on one of the following:
- Momentum—the investors try to use the continuance of the existing market trend to determine their positions
- Mean-reversion – the investors assume that properties such as stock returns and volatility will revert to their long-term average over time (also known as an Ornstein-Uhlenbeck process)
While we can relatively easily classify a time series as one of the two by inspecting it visually, this solution definitely does not scale well. That is why we can use approaches such as the Hurst exponent to identify if a given time series (not necessarily a financial one) is trending, mean-reverting, or simply a random walk.
A random walk is a process in which a path consists of a succession of steps taken at random. Applied to stock prices, it suggests that changes in stock prices have the same distribution...
