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It is now known that a seemingly random irregular time series can be deterministic chaos (hereafter, chaos). However, there can be various kind of noise superimposed into signals from real systems. Other factors affecting a signal include sampling intervals and finite length of observation. Perhaps, there may be cases in which a chaotic time series is considered as noise. J. Theiler proposed a method of surrogating data to address these problems. The proposed method is one of a number of approaches for testing a statistical hypothesis. The method can identify the deterministic characteristics of a time series. In this approach, a surrogate data is formed to have stochastic characteristics with the statistic value associated with the original data. When the characteristics of the original data differs from that of a surrogate data, the null hypothesis is no longer valid. In other words, the original data is deterministic. In comparing the characteristics of an original time series data and that of a surrogate data, the maximum Lyapunov exponents, correlation dimensions and prediction accuracy are utilized. These techniques, however, can not calculate the structure in local subspaces on the attractor and the flow of trajectories. In deal with these issues, we propose the trajectory parallel measure (TPM) method to determine whether the null hypothesis should be rejected. In this paper, we apply the TPM method and the method of surrogate data to test a chaotic time series and a random time series. We also examine whether a practical time series has a deterministic property or not. The results demonstrate that the TPM method is useful for judging whether the original and the surrogate data sets are different. For illustration, the TPM method is applied to a practical time series, tap water demand data.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.2 pp.343-349

- Publication Date
- 2000/02/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Intelligent Signal and Image Processing)

- Category

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Yasunari FUJIMOTO, Tadashi IOKIBE, "Evaluation of Deterministic Property of Time Series by the Method of Surrogate Data and the Trajectory Parallel Measure Method" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 2, pp. 343-349, February 2000, doi: .

Abstract: It is now known that a seemingly random irregular time series can be deterministic chaos (hereafter, chaos). However, there can be various kind of noise superimposed into signals from real systems. Other factors affecting a signal include sampling intervals and finite length of observation. Perhaps, there may be cases in which a chaotic time series is considered as noise. J. Theiler proposed a method of surrogating data to address these problems. The proposed method is one of a number of approaches for testing a statistical hypothesis. The method can identify the deterministic characteristics of a time series. In this approach, a surrogate data is formed to have stochastic characteristics with the statistic value associated with the original data. When the characteristics of the original data differs from that of a surrogate data, the null hypothesis is no longer valid. In other words, the original data is deterministic. In comparing the characteristics of an original time series data and that of a surrogate data, the maximum Lyapunov exponents, correlation dimensions and prediction accuracy are utilized. These techniques, however, can not calculate the structure in local subspaces on the attractor and the flow of trajectories. In deal with these issues, we propose the trajectory parallel measure (TPM) method to determine whether the null hypothesis should be rejected. In this paper, we apply the TPM method and the method of surrogate data to test a chaotic time series and a random time series. We also examine whether a practical time series has a deterministic property or not. The results demonstrate that the TPM method is useful for judging whether the original and the surrogate data sets are different. For illustration, the TPM method is applied to a practical time series, tap water demand data.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_2_343/_p

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@ARTICLE{e83-a_2_343,

author={Yasunari FUJIMOTO, Tadashi IOKIBE, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Evaluation of Deterministic Property of Time Series by the Method of Surrogate Data and the Trajectory Parallel Measure Method},

year={2000},

volume={E83-A},

number={2},

pages={343-349},

abstract={It is now known that a seemingly random irregular time series can be deterministic chaos (hereafter, chaos). However, there can be various kind of noise superimposed into signals from real systems. Other factors affecting a signal include sampling intervals and finite length of observation. Perhaps, there may be cases in which a chaotic time series is considered as noise. J. Theiler proposed a method of surrogating data to address these problems. The proposed method is one of a number of approaches for testing a statistical hypothesis. The method can identify the deterministic characteristics of a time series. In this approach, a surrogate data is formed to have stochastic characteristics with the statistic value associated with the original data. When the characteristics of the original data differs from that of a surrogate data, the null hypothesis is no longer valid. In other words, the original data is deterministic. In comparing the characteristics of an original time series data and that of a surrogate data, the maximum Lyapunov exponents, correlation dimensions and prediction accuracy are utilized. These techniques, however, can not calculate the structure in local subspaces on the attractor and the flow of trajectories. In deal with these issues, we propose the trajectory parallel measure (TPM) method to determine whether the null hypothesis should be rejected. In this paper, we apply the TPM method and the method of surrogate data to test a chaotic time series and a random time series. We also examine whether a practical time series has a deterministic property or not. The results demonstrate that the TPM method is useful for judging whether the original and the surrogate data sets are different. For illustration, the TPM method is applied to a practical time series, tap water demand data.},

keywords={},

doi={},

ISSN={},

month={February},}

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TY - JOUR

TI - Evaluation of Deterministic Property of Time Series by the Method of Surrogate Data and the Trajectory Parallel Measure Method

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 343

EP - 349

AU - Yasunari FUJIMOTO

AU - Tadashi IOKIBE

PY - 2000

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E83-A

IS - 2

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - February 2000

AB - It is now known that a seemingly random irregular time series can be deterministic chaos (hereafter, chaos). However, there can be various kind of noise superimposed into signals from real systems. Other factors affecting a signal include sampling intervals and finite length of observation. Perhaps, there may be cases in which a chaotic time series is considered as noise. J. Theiler proposed a method of surrogating data to address these problems. The proposed method is one of a number of approaches for testing a statistical hypothesis. The method can identify the deterministic characteristics of a time series. In this approach, a surrogate data is formed to have stochastic characteristics with the statistic value associated with the original data. When the characteristics of the original data differs from that of a surrogate data, the null hypothesis is no longer valid. In other words, the original data is deterministic. In comparing the characteristics of an original time series data and that of a surrogate data, the maximum Lyapunov exponents, correlation dimensions and prediction accuracy are utilized. These techniques, however, can not calculate the structure in local subspaces on the attractor and the flow of trajectories. In deal with these issues, we propose the trajectory parallel measure (TPM) method to determine whether the null hypothesis should be rejected. In this paper, we apply the TPM method and the method of surrogate data to test a chaotic time series and a random time series. We also examine whether a practical time series has a deterministic property or not. The results demonstrate that the TPM method is useful for judging whether the original and the surrogate data sets are different. For illustration, the TPM method is applied to a practical time series, tap water demand data.

ER -