The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Kini diketahui bahawa siri masa tidak teratur yang kelihatan rawak boleh menjadi huru-hara yang menentukan (selepas ini, huru-hara). Walau bagaimanapun, terdapat pelbagai jenis bunyi yang ditindih ke dalam isyarat daripada sistem sebenar. Faktor lain yang mempengaruhi isyarat termasuk selang pensampelan dan panjang pemerhatian terhingga. Mungkin, mungkin terdapat kes di mana siri masa huru-hara dianggap sebagai bunyi bising. J. Theiler mencadangkan kaedah penggantian data untuk menangani masalah ini. Kaedah yang dicadangkan adalah salah satu daripada beberapa pendekatan untuk menguji hipotesis statistik. Kaedah ini boleh mengenal pasti ciri-ciri penentu bagi siri masa. Dalam pendekatan ini, data pengganti dibentuk untuk mempunyai ciri stokastik dengan nilai statistik yang dikaitkan dengan data asal. Apabila ciri-ciri data asal berbeza daripada data pengganti, hipotesis nol tidak lagi sah. Dengan kata lain, data asal adalah deterministik. Dalam membandingkan ciri data siri masa asal dan data pengganti, eksponen Lyapunov maksimum, dimensi korelasi dan ketepatan ramalan digunakan. Teknik ini, bagaimanapun, tidak dapat mengira struktur dalam subruang tempatan pada penarik dan aliran trajektori. Dalam menangani isu ini, kami mencadangkan kaedah ukuran selari trajektori (TPM) untuk menentukan sama ada hipotesis nol harus ditolak. Dalam kertas kerja ini, kami menggunakan kaedah TPM dan kaedah data pengganti untuk menguji siri masa huru-hara dan siri masa rawak. Kami juga mengkaji sama ada siri masa praktikal mempunyai sifat deterministik atau tidak. Keputusan menunjukkan bahawa kaedah TPM berguna untuk menilai sama ada set data asal dan pengganti adalah berbeza. Sebagai ilustrasi, kaedah TPM digunakan pada siri masa praktikal, data permintaan air paip.
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Salinan
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
Salinan
@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},}
Salinan
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 -