Trends/Statistics and risk

Hurst exponent

A number that says whether a series tends to trend (above 0.5), reverse (below 0.5) or move randomly (about 0.5).

Statistics and riskBest on 3Y, 5YAlso called H

Illustration of the Hurst exponent shape. It is a sketch, not real price data.

What it shows

The Hurst exponent comes from the study of the Nile's floods by Harold Hurst. It looks at how the range of a series grows with the length of time. A value of 0.5 is a random walk. Above 0.5 the series has persistence: moves tend to continue. Below 0.5 it is mean-reverting.

It is estimated from the last 252 to 500 bars. Estimates are noisy.

How we find it

The same code that draws it on your chart follows these steps, with the same result every time.

Split the returns into windows of different lengths.
For each, compute the rescaled range (R/S).
Fit log(R/S) against log(window length).
The slope is the Hurst exponent.

Starting values: Window 500 bars; Method rescaled range. These are proposed and will be tuned on real price data before launch.

How to read it

The panel shows H over time.
The dashed line is 0.5.
Above: trending. Below: reverting.

Status labels you may see

Label	What it means
Persistent	H above 0.55.
Random	0.45 to 0.55.
Mean-reverting	H below 0.45.

What cancels it

Nothing cancels it.

What traders check next

Window length.
Autocorrelation.
Method used.

Limits

Noisy and biased in short samples.
Different methods give different values.
Does not predict direction.

Try it in forecastviz

Open any ticker and choose Statistics and risk → Hurst exponent in the left menu.
Switch between 3Y, 5Y to see how the picture changes.
Compare with Autocorrelation and Efficiency ratio on the same chart.

Open on a ticker

Questions

Is 0.5 special?

It is the value for a random walk.

Can I trust the number?

Treat as rough.