Rescaled Range

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Rescaled Range (R/S) Analysis

The analysis developed by H.E. Hurst to determine long-memory effects and fractional Brownian motion. Rescaled range analysis measures how the distance covered by a particle increases as we look at longer and longer time scales. For Brownian motion, the distance covered increases with the square root of time. A series which increases at a different rate is not random. See: Anti-persistence, Fractional Brownian Motion, Hurst Exponent, Persistence, Joseph Effect, Noah Effect.

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In this study, we estimate the fractal dimension of price returns and test the Efficient Market Hypothesis (EMH), employing rescaled range analysis in order to use fewer assumptions about the underlying system.

We used a rescaled range (R/S) analysis in this study to estimate it.

Stock market behavior: a fractal analysis of Saudi Stock Exchange

Hurst (1951) developed the rescaled range technique for time series analysis.

tau]] average rescaled range for a subperiod of length [tau] [R.

Flow regime determination in horizontal hydrotransport using non-intrusive acoustic probes

This paper examines the efficacy of the statistical measures of risk in the light of results obtained from the analysis of stock market data using contemporary techniques of mathematical modelling of dynamical systems like the Rescaled Range Analysis and the related Hurst's Exponent, Fractal Dimensions, and the Lyapunov Exponents.

Risk measurement, nonlinearities, and chaos

The Rescaled Range (R/S) analysis is a powerful indicator of the persistence of a series where the influence of a set of past price changes on a set of future price changes is effectively captured.

When properly normalized, as the sample size n increases without bound, the rescaled range converges in distribution to a well-defined random variable V, that is,

Nuances of chaos in foreign exchange markets

Relevant tests employed include neural networks, correlation dimensions, Lyapunov exponents, fractional integration and rescaled range.

New Book Provides Insights into the Modeling and Forecasting of Primary Commodity Prices

The work presented in this paper was conducted to compare the suitability of statistical, mutual information function, spectral and Hurst's Rescaled Range analysis for discrimination of flow regime transitions in a semi-cylindrical gas-solid spouted bed.

Pressure fluctuation time series recorded at several axial positions and operating conditions were analyzed by statistical, mutual information theory, spectral and Hurst's Rescaled Range methods in an effort to detect signal properties useful for discrimination of flow regimes transitions in gas-solid spouted beds.

Evaluation of flow regimes in a semi-cylindrical spouted bed through statistical, mutual information, spectral and Hurst's analysis

The Modified Rescaled Range (R/S) analysis is a powerful indicator of long-term persistence of a series where the influence of a set of past returns on a set of future returns is effectively captured.

The Rescaled Range analysis is based on the simple hypothesis that any IID data would show an increase in standardized ranges which are proportional to increase in sample sizes as samples of increasing subperiod lengths are considered.