Why Hurst R/S Analysis Usually Uses Returns Instead of Prices

Summary

The document asks how to estimate a stock’s Hurst exponent using rescaled range (R/S) analysis. The author reports that applying the method directly to Apple and Google price series from 2010 to 2017 produced estimates above 0.9, while applying it to daily log returns produced an estimate around 0.5. They ask whether the difference is related to price nonstationarity and return stationarity.

These examples motivate checking the properties of the input series before interpreting an R/S estimate: price levels can trend and may yield misleading evidence of persistence, whereas returns are often analyzed as a more stationary series. The post does not provide an answer, describe the calculation details, or establish that the reported estimates are robust. The stationarity of returns is an assumption to test, not a guarantee, and an estimate near 0.5 does not by itself prove that returns are independent or that the market is efficient.

Key ideas

• R/S analysis applied to stock price levels can produce a high Hurst estimate when the series is nonstationary.
• The author reports a value around 0.5 when using daily log returns for the two example stocks.
• The post raises stationarity as a possible explanation but does not resolve the question.
• Series choice and diagnostic checks matter when interpreting Hurst estimates.

Tags

# Hurst exponent of stock using R/S analysis


# Hurst exponent of stock using R/S analysis












I am attempting to use R/S analysis to estimate the Hurst Exponent on a single stock.

At first I directly use the stock price ( instead of stock return) and the Hurst component calculated is > 0.9 ( used Apple, Google respectively from 2010 to 2017) which seems to be incorrect.

Then I tried to use log return(daily) instead and the result is around 0.5 which seems normal.

So I should use return instead of stocks price but why? Is this related to stationarity of the time series?( I believe stock price is clearly non-stationary and return is stationary)

Thanks.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.