On Dimension Estimates with Surrogate Data Sets

Tohru IKEGUCHI; Kazuyuki AIHARA

On Dimension Estimates with Surrogate Data Sets

Tohru IKEGUCHI, Kazuyuki AIHARA

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In this paper, we propose a new strategy of estimating correlation dimensions in combination with the method of surrogate data, which is a kind of statistical control usually introduced to avoid spurious estimates of nonlinear statistics, such as fractal dimensions, Lyapunov exponents and so on. In the case of analyzing time series with the method of surrogate data, it is desirable to decide values of estimated nonlinear statistics of the original data and surrogate data sets as exactly as possible. However, when dimensional analysis is applied to possible attractors reconstructed from real time series, it is very dangerous to decide a single value as the estimated dimensions and desirable to analyze its scaling property for avoiding spurious estimates. In order to solve this defficulty, a dimension estimator algorithm and the method of surrogate data are combined by introducing Monte Carlo hypothesis testing. In order to show effectiveness of the new strategy, firstly artificial time series are analyzed, such as the Henon map with additive noise, filtered random numbers and filtered random numbers transformed by a static monotonic nonlinearity, and then experimental time series are also examined, such as wolfer's sunspot numbers and the fluctuations in a farinfrared laser data.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E80-A No.5 pp.859-868

Publication Date: 1997/05/25

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Category: Nonlinear Problems

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Tohru IKEGUCHI, Kazuyuki AIHARA, "On Dimension Estimates with Surrogate Data Sets" in IEICE TRANSACTIONS on Fundamentals, vol. E80-A, no. 5, pp. 859-868, May 1997, doi: .
Abstract: In this paper, we propose a new strategy of estimating correlation dimensions in combination with the method of surrogate data, which is a kind of statistical control usually introduced to avoid spurious estimates of nonlinear statistics, such as fractal dimensions, Lyapunov exponents and so on. In the case of analyzing time series with the method of surrogate data, it is desirable to decide values of estimated nonlinear statistics of the original data and surrogate data sets as exactly as possible. However, when dimensional analysis is applied to possible attractors reconstructed from real time series, it is very dangerous to decide a single value as the estimated dimensions and desirable to analyze its scaling property for avoiding spurious estimates. In order to solve this defficulty, a dimension estimator algorithm and the method of surrogate data are combined by introducing Monte Carlo hypothesis testing. In order to show effectiveness of the new strategy, firstly artificial time series are analyzed, such as the Henon map with additive noise, filtered random numbers and filtered random numbers transformed by a static monotonic nonlinearity, and then experimental time series are also examined, such as wolfer's sunspot numbers and the fluctuations in a farinfrared laser data.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e80-a_5_859/_p

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@ARTICLE{e80-a_5_859,
author={Tohru IKEGUCHI, Kazuyuki AIHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On Dimension Estimates with Surrogate Data Sets},
year={1997},
volume={E80-A},
number={5},
pages={859-868},
abstract={In this paper, we propose a new strategy of estimating correlation dimensions in combination with the method of surrogate data, which is a kind of statistical control usually introduced to avoid spurious estimates of nonlinear statistics, such as fractal dimensions, Lyapunov exponents and so on. In the case of analyzing time series with the method of surrogate data, it is desirable to decide values of estimated nonlinear statistics of the original data and surrogate data sets as exactly as possible. However, when dimensional analysis is applied to possible attractors reconstructed from real time series, it is very dangerous to decide a single value as the estimated dimensions and desirable to analyze its scaling property for avoiding spurious estimates. In order to solve this defficulty, a dimension estimator algorithm and the method of surrogate data are combined by introducing Monte Carlo hypothesis testing. In order to show effectiveness of the new strategy, firstly artificial time series are analyzed, such as the Henon map with additive noise, filtered random numbers and filtered random numbers transformed by a static monotonic nonlinearity, and then experimental time series are also examined, such as wolfer's sunspot numbers and the fluctuations in a farinfrared laser data.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - On Dimension Estimates with Surrogate Data Sets
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 859
EP - 868
AU - Tohru IKEGUCHI
AU - Kazuyuki AIHARA
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 1997
AB - In this paper, we propose a new strategy of estimating correlation dimensions in combination with the method of surrogate data, which is a kind of statistical control usually introduced to avoid spurious estimates of nonlinear statistics, such as fractal dimensions, Lyapunov exponents and so on. In the case of analyzing time series with the method of surrogate data, it is desirable to decide values of estimated nonlinear statistics of the original data and surrogate data sets as exactly as possible. However, when dimensional analysis is applied to possible attractors reconstructed from real time series, it is very dangerous to decide a single value as the estimated dimensions and desirable to analyze its scaling property for avoiding spurious estimates. In order to solve this defficulty, a dimension estimator algorithm and the method of surrogate data are combined by introducing Monte Carlo hypothesis testing. In order to show effectiveness of the new strategy, firstly artificial time series are analyzed, such as the Henon map with additive noise, filtered random numbers and filtered random numbers transformed by a static monotonic nonlinearity, and then experimental time series are also examined, such as wolfer's sunspot numbers and the fluctuations in a farinfrared laser data.
ER -