{"id":5301,"date":"2013-01-30T06:26:59","date_gmt":"2013-01-30T11:26:59","guid":{"rendered":"http:\/\/www.jasonapollovoss.local\/?p=5301"},"modified":"2020-04-09T07:16:28","modified_gmt":"2020-04-09T11:16:28","slug":"rescaled-range-analysis-a-method-for-detecting-persistence-randomness-or-mean-reversion-in-financial-markets","status":"publish","type":"post","link":"https:\/\/jasonapollovoss.com\/web\/2013\/01\/30\/rescaled-range-analysis-a-method-for-detecting-persistence-randomness-or-mean-reversion-in-financial-markets\/","title":{"rendered":"Rescaled Range Analysis: A Method for Detecting Persistence, Randomness, or Mean Reversion in Financial Markets"},"content":{"rendered":"

Editor’s note: Thanks to the diligence of Armin Grueneich this post has been amended to reflect\u00a0the addition of\u00a0step #5, below,\u00a0in the calculation of the rescaled range.<\/em><\/span><\/p>\n

Rescaled range analysis is a statistical technique designed to assess the nature and magnitude of variability in data over time. In investing rescaled range analysis has been used to detect and evaluate the amount of persistence, randomness, or mean reversion in financial markets time series data. Insight of this kind into financial data naturally suggests investment strategies.<\/span><\/p>\n

Originally invented for the field of hydrology by Harold Edwin Hurst<\/a>, the technique was developed to predict Nile River flooding in advance of the construction of the Aswan High Dam. The dam needed to fulfill multiple and divergent purposes, including serving as both a store of water to protect against drought for farmers down river, and as flood protection for those same farmers during typical annual flooding. Rainfall levels in Central Africa were seemingly random each year, yet the Nile River flows seemed to show autocorrelation<\/a>. That is, rainfall in one time period seemed to influence rainfall in subsequent periods. Hurst needed to be able to see if there was a hidden long-term trend \u2014 statistically known as a long-memory process<\/em> \u2014 in the Nile River data that might guide him in building a better dam for Egypt.<\/span><\/p>\n

Does this sound familiar? A time series of varying levels that is seemingly random but in which it is suspected that there might also be a long-term, hidden trend. Not surprisingly rescaled range analysis had its moment in the financial analysis sun in the mid-1990s, when chaos theory, as applied to financial markets was a hot topic. Chaos theory<\/a> is a branch of science that studies the interconnectedness of events that otherwise, on the surface, seem random.<\/span><\/p>\n

Closely associated with rescaled range analysis is the Hurst exponent<\/a>, indicated by H<\/em>, also known as the \u201cindex of dependence\u201d or the \u201cindex of long-range dependence.\u201d A Hurst exponent ranges between 0 and 1, and measures three types of trends in a time series: persistence, randomness, or mean reversion.<\/span><\/p>\n