Hurst Exponent – Checking for Trend Persistance – Python Notebook

Hurst exponent is originally developed by the famous hydrologist Harold Edwin Hurst to study the Long-Term Storage Capacity of Reservoirs. Hurst is developed to model reservoirs but later found to be used in other natural systems to measure the long term memory of time series.

Hurst was looking for a better way to model the levels of the river Nile to construct an appropriately sized reservoir system.

In a Hurst Exponent is used to determining the trend persistence (i.e whether a given time series is trending, mean-reverting or random series)

How to Read Hurst Exponent Values?

Hurst value ranges between 0 < H < 1

i) Trending: If the Hurst value range is between 0.5 < H < 1 indicates persistence in time series. The higher the value of the Hurst exponent more the trendiness of the market structure. For values close to 1 the series is persistent.

ii) Mean Reverting: If the Hurst value range is between 0 < H < 0.5 indicates anti persistence in time series. The lower the value of the Hurst exponent more the mean-reverting behavior (trend reversal). For values close to 0, the series is anti-persistent

iii) Geometrical Brownian Motion: It explains the random walk with the l unpredictability of the time series. If Hurst Exponent value is H = 0.5 then the time series is expected to move in a random walk.

Geometric Brownian Motion is widely used to model stock prices in finance

Jupyter Python Notebook to compute Hurst Exponent for Nifty

More Readings on Hurst Exponent

1. H.E. Hurst, 1951, “Long-term storage of reservoirs: an experimental study,” Transactions of the American Society of Civil Engineers, Vol. 116, pp. 770-799.
2. Bo Qian, Khaled Rasheed, 2004, “Hurst Exponent and financial market predictability,” IASTED conference on “Financial Engineering and Applications”(FEA 2004), pp. 203-209,
3. Mandelbrot, Benoit B., 2004, “The (Mis)Behavior of Markets, A Fractal View of Risk, Ruin and Reward,” Basic Books, 2004.
4. Miguel Ángel Sánchez1, Juan E. Trinidad2, José García2, Manuel Fernández, 2015, “The Effect of the Underlying Distribution in Hurst Exponent Estimation”