Long-range correlation properties of stationary linear models with mixed periodicities

Tomomichi Nakamura, Michael Small, Toshihiro Tanizawa

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider the problem of (stationary and linear) source systems which generate time series data with long-range correlations. We use the discrete Fourier transform (DFT) and build stationary linear models using artificial time series data exhibiting a 1/f spectrum, where the models can include only terms that contribute significantly to the model as assessed by information criteria. The result is that the optimal (best) model is only composed of mixed periodicities [that is, the model does not include all (continuous) periodicities] and the time series data generated by the model exhibit a clear 1/f spectrum in a wide frequency range. It is considered that as the 1/f spectrum is a consequence of the contributions of all periods, consecutive periods are indispensable to generate such data by stationary linear models. However, the results indicate that there are cases where this expectation is not always met. These results also imply that although we can know linear features of time series data using the DFT, we always cannot substantially infer the type of the source system, even if the system is stationary linear.

Original languageEnglish
Article number022128
Number of pages6
JournalPhysical Review E
Volume99
Issue number2
DOIs
Publication statusPublished - 19 Feb 2019

Cite this

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title = "Long-range correlation properties of stationary linear models with mixed periodicities",
abstract = "We consider the problem of (stationary and linear) source systems which generate time series data with long-range correlations. We use the discrete Fourier transform (DFT) and build stationary linear models using artificial time series data exhibiting a 1/f spectrum, where the models can include only terms that contribute significantly to the model as assessed by information criteria. The result is that the optimal (best) model is only composed of mixed periodicities [that is, the model does not include all (continuous) periodicities] and the time series data generated by the model exhibit a clear 1/f spectrum in a wide frequency range. It is considered that as the 1/f spectrum is a consequence of the contributions of all periods, consecutive periods are indispensable to generate such data by stationary linear models. However, the results indicate that there are cases where this expectation is not always met. These results also imply that although we can know linear features of time series data using the DFT, we always cannot substantially infer the type of the source system, even if the system is stationary linear.",
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Long-range correlation properties of stationary linear models with mixed periodicities. / Nakamura, Tomomichi; Small, Michael; Tanizawa, Toshihiro.

In: Physical Review E, Vol. 99, No. 2, 022128, 19.02.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Long-range correlation properties of stationary linear models with mixed periodicities

AU - Nakamura, Tomomichi

AU - Small, Michael

AU - Tanizawa, Toshihiro

PY - 2019/2/19

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N2 - We consider the problem of (stationary and linear) source systems which generate time series data with long-range correlations. We use the discrete Fourier transform (DFT) and build stationary linear models using artificial time series data exhibiting a 1/f spectrum, where the models can include only terms that contribute significantly to the model as assessed by information criteria. The result is that the optimal (best) model is only composed of mixed periodicities [that is, the model does not include all (continuous) periodicities] and the time series data generated by the model exhibit a clear 1/f spectrum in a wide frequency range. It is considered that as the 1/f spectrum is a consequence of the contributions of all periods, consecutive periods are indispensable to generate such data by stationary linear models. However, the results indicate that there are cases where this expectation is not always met. These results also imply that although we can know linear features of time series data using the DFT, we always cannot substantially infer the type of the source system, even if the system is stationary linear.

AB - We consider the problem of (stationary and linear) source systems which generate time series data with long-range correlations. We use the discrete Fourier transform (DFT) and build stationary linear models using artificial time series data exhibiting a 1/f spectrum, where the models can include only terms that contribute significantly to the model as assessed by information criteria. The result is that the optimal (best) model is only composed of mixed periodicities [that is, the model does not include all (continuous) periodicities] and the time series data generated by the model exhibit a clear 1/f spectrum in a wide frequency range. It is considered that as the 1/f spectrum is a consequence of the contributions of all periods, consecutive periods are indispensable to generate such data by stationary linear models. However, the results indicate that there are cases where this expectation is not always met. These results also imply that although we can know linear features of time series data using the DFT, we always cannot substantially infer the type of the source system, even if the system is stationary linear.

KW - 1/F NOISE

KW - TIME-SERIES

KW - NONLINEARITY

U2 - 10.1103/PhysRevE.99.022128

DO - 10.1103/PhysRevE.99.022128

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JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

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SN - 1539-3755

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