Improve Hurst Exponent to Evaluate the Information Efficiency of Companies in Fractal Markets

Subject and Purpose of the Article: 

In this study, using simulated data of fractal time series (ARFIMA) in R software to investigate the new Hurst criterion to evaluate the efficiency of fractal markets in private and public companies has been researched.

This simulation is introduced using the assumed parameter dimension of the new measurement criterion by changing and optimizing the Hurst criterion by changing the focus index and the middle substitution instead of the mean, and by using the data simulation it is shown that The reason for the intrinsic characteristics of the middle and its independence from severe data  fluctuations is more accurate and less deviation than the previous criterion in identifying the fractal dimensions of the market for all public and private companies.

Finally, it has been observed that the new criterion in calculating market   efficiency using the change in Hurst criterion is closer to the reality that we have already simulated and has less deviation.

Conclusion, Originality and its Contribution to the Knowledge: 

In this study, it was shown that the variance of the Hurst R/S estimator using the mean index is higher than the variance of the   corresponding estimator using the median index. As a result, the accuracy of the newly introduced estimator is higher than the previous computational methods.