Hello there:
I have just recently seen the lectures regarding the Hurst exponent… in fact, there is a document that expain how to calculate this exponent step by step with a sample if stock data.
I used the exact same procedure as the example, to calculate the Hurst exponent, and I got a value of 1,041… that is… I got a Hurst exponent greater than one…
Whatt does this mean?? I mean the explanation says that when the Hurst exponent is less than 0,5 it is a mean reverting stock data, and it is trending if it is higher that 0,5
But what about the trending if the Hurst exponent is greater than one??
A ratio greater than 1 has not much theoretical interpretation or physical significance in describing the generating process. Hurst exponent range that makes sense should be a fraction below 1. On the first look, it looks like a data input issue. If you look at the definition of hurst exponent, the most likely way the ratio can be greater than 1 is you have a residual trend in the input series. This can happen if the input data series was not stationary, or the de-trending did not work. I think the way hurst exponent is calculated, it is susceptible to errors even if you have done standard operations to generate a stationary series. For example, long memory parameters can be misguided if the input series is short, or there are regime changes/ jump clustering. May be use a longer timeseries and check for any large permanent jump in the input.
Ok, thanks for the answer… but consider Urban One Inc. (NASDAQ:UONE), if you calculate the Hurst exponent using 9 data (from 5/24/21 to 6/4/21), you will obtain that it turns out to be 1,0668921.
So do you think the trend will persist?? yes ??, no?? and why??