Click on the link below for some assistance:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.137.207&rep=rep1&type=pdf

Another issue is that the Hurst/d-statistic cannot distinguish between long-memory and structural breaks; in that case, you might want to also check if there's a structural break using the Bai-Perron method, which allows for multiple structural breaks. Also, I remember hearing a presentation by Chris Heyde back in 1999 where he documented the long memory in the S&P 500, before proposing a continuous time process that accounts for that long-memory. But even here, if you take a continuous time way of thinking about trading strategies, I think you wouldn't buy and hold if the investment opportunity set changes, and I think that's probably a good reason why people trade, even if they don't explain what they're doing in such terms.

I think Hurst exponent is a good stock classifier, based in some references. For exemple, remembering that D=2-H where D is fractal dimension, stocks with more roughness (with H below 1 in direction to 0) suggest more "up and down" regimes and more possibilites to make a by-and-hold strategy. Another reference suggests that Hurst exponent calculated from returns shows the "nervouness" in the market when H

Thanks for all answers!

Dear William

I have just one point to make, one school of thought confirms that since stock price varies multiple times during one day so it cannot be a true time series. In that case Hurst Exponent is not proper.

However another group of experts suggest that though the stock prices have gone up and down many a times in a day yet only the closing is recorded for reference, so Hurst exponent will function quite accurately.

According to me, run it one past data and then calculate outliers with Mahalanobis Distance. If the outliers are substantially on the lower side, then Hurst exponent will surely be used.

 Regards

Bikram

Thanks for your contribution Ghosh.

Some researchers study the Hurst Exponent and other scaling exponent in intraday time series and compare the dynamics with stock's closing prices. They found different dynamics with different behaviour depending the time window analysis. This is well-know by "multifractals": if the stock behaviour was pure fractal, all time serie lenght analysis will show the same fractal dimension (or the same Hurst exponent), but this is not true and our sence confirm this. Considering that stock time series is multifractal, we can find different dynamics depending the lenght of time serie and we could find a totally different dynamic in intraday time series.

I would like to know more about Mahalanobis Distance. Can you send some refeference for us?

Hello,

I think "multifractals" will be quite accurate for strong efficient or semi strong efficient stock markets. But if you carry out the same study in a distinctly diverse, highly heterogeneous and sentimentally driven capital market, then some or many a latent variables will create a large base of outliers. Which will make the fitment of that model inaccurate. So they call rests on the type of capital market under consideration. Again one more aspect within that segmentation will be more analysis is done one Large Caps and Mid Caps, however the so called penny stocks are not quite well researched upon. So, even within the same economy the Large Cap predictability model in an intraday space will be distinctly different from that of a small cap or micro cap.

For Mahalanobis Distance- I found two practical papers out of many present in Google Scholar. These may help you.

http://www.sciencedirect.com/science/article/pii/S0169743999000477

http://link.springer.com/article/10.1007/s00170-005-0004-2

Warm Regards

Bikram

Depends on what types of analysis, you want to do. You will find an example:

https://www.sciencedirect.com/science/article/abs/pii/S037843711932014X