Detrending Moving Average variance: a derivation of the scaling law

Sergio Arianos; Anna Carbone

doi:10.1016/j.physa.2007.02.074

paper

Detrending Moving Average variance: a derivation of the scaling law

arXiv:physics/0608313 · doi:10.1016/j.physa.2007.02.074

Abstract

The Hurst exponent $H$ of long range correlated series can be estimated by means of the Detrending Moving Average (DMA) method. A computational tool defined within the algorithm is the generalized variance $σ_{D M A}^{2} = 1 / (N - n) \sum_{i} [y (i) - y_{n} (i)]^{2}$ , with $y_{n} (i) = 1 / n \sum_{k} y (i - k)$ the moving average, $n$ the moving average window and $N$ the dimension of the stochastic series $y (i)$ . This ability relies on the property of $σ_{D M A}^{2}$ to scale as $n^{2 H}$ . Here, we analytically show that $σ_{D M A}^{2}$ is equivalent to $C_{H} n^{2 H}$ for $n ≫ 1$ and provide an explicit expression for $C_{H}$ .

arXiv comment11pages, 3 figures. Presented at Int. Conf. on Application of Physics in Financial Analisys (APFA5), June 29 - July 1, 2006 Torino, Italy

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An integrated approach to the assessment of long range correlation in time series data

Detrending Moving Average variance: a derivation of the scaling law

Abstract

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