# Rescaled Range Analysis - Explained

What is a Rescaled Range Analysis?

# What is a Rescaled Range Analysis?

Rescaled range analysis is a statistical technique used in assessing the nature and analyze the variability of a time series. Harold Edwin Hurst, a British hydrologist developed the rescaled range analysis. At the time the analysis was developed, it was to forecast flooding in river Nile, however, the analysis has become a statistical technique used in evaluating the level of persistence or randomness in the financial markets. Investors also use this analysis to analyze patterns, trends, and cycles in the financial markets as pertaining to the prices of stocks and bonds.

## How Does a Rescaled Range Analysis Work?

The rescaled range analysis can be used to analyze trends in the financial market time series data with the purpose of knowing the level of mean reversion present in the market. This analysis also helps investors and financial analysts determine the amount of randomness or persistence in the market. Given that the financial markets are not perfectly efficient, changes could occur in the time series data. In the rescaled range analysis the Hurst exponent otherwise called H exponent is the index of long-range dependence which captures strong trends, patterns, and cycles in the time series data. The H exponent also measures the amount of persistence, randomness and mean reversion in the financial markets time series data. The H exponent ranges from 0 to 1, a range greater than 0.5 shows a long-term trend while a range of less than 0.5 indicates that a reversal could occur in the trend over a period of time.

## Trading the Hurst Exponent

Investors use the Hurst Exponent to as an investment strategy and this also influences their investment decisions. Essentially, algorithmic traders use the H exponent to evaluate the mean reversion of time series with the intention of capitalizing on the changes in the security price. The use of the H exponent also varies from investor to investor, for instance, active or growth investors are likely to use the H exponent in a dimension different from that of the passive investors. A growth investor is often focused on stocks that have H 0.5, as this indicates strong trends and persistence in the market. On the other hand, stocks with H < 0.5 can be attractive to Value investors.

## Calculating Rescaled Range

The Rescaled Range is calculated for a time series, , as follows: Calculate the mean for each range Create a mean adjusted series Create a series which is the running total of the deviations from the mean Create a range series R, which is the widest difference in the series of deviations Create a standard deviation series S; Where m(t) is the mean for the time series values through time Calculate the rescaled range series (R/S)