# Trends in Stock Prices and Range to Standard Deviation Ratio

The Hurst was proposed in 1951 by Hurst. “The Hurst exponent provides a measure for long-term memory and predictability of a time series.”(Mitra 2011) The Hurst exponent was used in hydrological studies, however in 1991 and 1994 Peters used the Hurst exponent in financial studies.

This article studies the Hurst exponent by developing insight on the price movements in financial markets by taking the Hurst exponent and returns in the stock market and comparing them. This is done to see if the R/S ratios are related to the return generating process in the stock market. They did this by watching the stock market for 10 years. The daily closing prices of different stock indices were taken daily over the ten year span.

“Hurst observed that the H-value directly depends on range to standard deviation ratio (R/S ratio). Thus R/S ratio can provide a method of classifying time series, which can be useful in identifying which markets have greater predictability.”(Mitra 2011M) It first had to be determined whether the time series that was under study was predictable. The study needed to be performed on a time series with predictability. A large R/S ratio in a time series has trending characteristics, this being more predictable that a low R/S ratio in a series.

Charts and tables were created to show the findings in the research. In the findings it was “determined that R/S ratios are related to the return generating process in the stock market. “(Mitra 2011)

The stock indices that were studied showed a Hurst exponent close to .5, this showing random behavior of market return. The R/S ratio in the 30 day- period window was to vary dynamically overtime. Whenever the R/S values were high, the average returns were also high.

Mitra, Subrata Kumar January 2011. International Journal of Business and Management6.1. Retrieved from http://search.proquest.com.ezproxy.apollolibrary.com/docview/848431519....

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