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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Band name Original scaling range Rescaled range Blue [0, 47] [0, 12] [47, 116] [12, 138] [116, 255] [138, 255] Hybrid green [0, 38] [0, 13] (F = 0.
Residuals of this estimated fundamental time series are then tested for possible speculative deviations using a Hamilton regime switching test and a rescaled range Hurst coefficient test, with a further test for nonlinearity beyond the ARCH effects using the BDS statistic.
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.
In the theory of chaotic systems different methods are used [5], among others such as: correlation dimension [15]; Kolmogorov entropy, Lapunov exponent, fractal dimension [13]; Brock-Dechert-Scheinkman's test, rescaled range analysis [8,9,10,12].
n](t), were determined by five methods: the rescaled range analysis (R/[sigma]), the roughness length (SD), the variogram (V), the power-spectrum (P), and the wavelet methods (W[X](a)).
Some studies (such as those by Peters, 1989; 1996) using classical rescaled range (or R/S) analysis have found evidence of long-term memory.
Hurst (1951) developed the rescaled range technique for time series analysis.
This work presents an application of rescaled range analysis (R/S) to study the fractal properties of precipitation in Venezuela.
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.
Long memory in foreign exchange markets is examined for the post-Bretton Woods period using Lo's [1991] modified rescaled range (R/S).
First proposed by Hurst (1951), the rescaled range technique has been applied to numerous time series of natural phenomena such as river levels and tree growth rates to measure the level of randomness in a system over time.
Relevant tests employed include neural networks, correlation dimensions, Lyapunov exponents, fractional integration and rescaled range.