Detrending Moving Average variance: a derivation of the scaling law
| dc.creator | Arianos, Sergio | |
| dc.creator | Carbone, Anna | |
| dc.date | 2006-08-31 | |
| dc.date.accessioned | 2026-07-07T12:54:28Z | |
| dc.date.available | 2026-07-07T12:54:28Z | |
| dc.description | 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_{DMA}^2={1}/{(N-n)}\sum_i [y(i)-\widetilde{y}_n(i)]^2\:$, with $\widetilde{y}_n(i)= {1}/{n}\sum_{k}y(i-k)$ 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 $σ_{DMA}^2$ to scale as $n^{2H}$. Here, we analytically show that $σ_{DMA}^2$ is equivalent to $C_H n^{2H}$ for $n\gg 1$ and provide an explicit expression for $C_H$. | |
| dc.description | 11pages, 3 figures. Presented at Int. Conf. on Application of Physics in Financial Analisys (APFA5), June 29 - July 1, 2006 Torino, Italy | |
| dc.identifier | https://arxiv.org/abs/physics/0608313 | |
| dc.identifier | http://arxiv.org/abs/physics/0608313 | |
| dc.identifier | Physica A: Statistical Mechanics and its Applications Volume 382, (2007) Pages 9-15 | |
| dc.identifier | doi:10.1016/j.physa.2007.02.074 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223944 | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.subject | Statistical Finance | |
| dc.title | Detrending Moving Average variance: a derivation of the scaling law | |
| dc.type | text |