Oscillating systems with cointegrated phase processes

Østergaard, Jacob; Rahbek, Anders; Ditlevsen, Susanne

doi:10.1007/s00285-017-1100-2

Cited by 8 publications

(12 citation statements)

References 30 publications

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“…Table 5 and Table 6 present the results that essentially lead to the same conclusions obtained by [ 45 ], even though they have based their findings on the trace test. See Table 8 of [ 45 ].…”

Section: Implementing the Fbst As A Cointegration Testsupporting

confidence: 76%

“…We analyzed four electroencephalography (EEG) signals from a subject that has previously presented epileptic seizures. The original study, [ 44 ], had the aim of detecting seizures based on multiple hours of recordings for each individual and the cointegration analysis of the mentioned signals was presented by [ 45 ]. In fact, the cointegration hypothesis is tested using the phase processes estimated from the original signals.…”

Section: Implementing the Fbst As A Cointegration Testmentioning

confidence: 99%

“…This is done by passing the signal into the Hilbert transform and then “unwrapping” the resulting transform. Sections 2 and 5 of [ 45 , 46 ] provide more details on the Hilbert transform and unwrapping.…”

Section: Implementing the Fbst As A Cointegration Testmentioning

confidence: 99%

“…The recordings of the studied subject, an 11-year-old female, identified a seizure in the interval (measured in seconds)

. Therefore, like [ 45 ], we analyze the period of 41 seconds prior to the seizure—interval

—and the subsequent 41 seconds—interval

—the seizure period. In the sequel, we will refer to these as prior to seizure and during seizure , respectively.…”

Section: Implementing the Fbst As A Cointegration Testmentioning

confidence: 99%

“…Figure 1 and Figure 2 display the estimated phases based on the original signals. The model proposed by [ 45 ] is a VAR(1), resulting in a VECM given by

…”

Section: Implementing the Fbst As A Cointegration Testmentioning

confidence: 99%

See 4 more Smart Citations

Cointegration and Unit Root Tests: A Fully Bayesian Approach

Diniz

Pereira

Stern³

2020

Entropy

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To perform statistical inference for time series, one should be able to assess if they present deterministic or stochastic trends. For univariate analysis, one way to detect stochastic trends is to test if the series has unit roots, and for multivariate studies it is often relevant to search for stationary linear relationships between the series, or if they cointegrate. The main goal of this article is to briefly review the shortcomings of unit root and cointegration tests proposed by the Bayesian approach of statistical inference and to show how they can be overcome by the Full Bayesian Significance Test (FBST), a procedure designed to test sharp or precise hypothesis. We will compare its performance with the most used frequentist alternatives, namely, the Augmented Dickey–Fuller for unit roots and the maximum eigenvalue test for cointegration.

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Section: Implementing the Fbst As A Cointegration Testsupporting

confidence: 76%

Section: Implementing the Fbst As A Cointegration Testmentioning

confidence: 99%

Section: Implementing the Fbst As A Cointegration Testmentioning

confidence: 99%

“…The recordings of the studied subject, an 11-year-old female, identified a seizure in the interval (measured in seconds)

. Therefore, like [ 45 ], we analyze the period of 41 seconds prior to the seizure—interval

—and the subsequent 41 seconds—interval

—the seizure period. In the sequel, we will refer to these as prior to seizure and during seizure , respectively.…”

Section: Implementing the Fbst As A Cointegration Testmentioning

confidence: 99%

“…Figure 1 and Figure 2 display the estimated phases based on the original signals. The model proposed by [ 45 ] is a VAR(1), resulting in a VECM given by

…”

Section: Implementing the Fbst As A Cointegration Testmentioning

confidence: 99%

See 3 more Smart Citations

Cointegration and Unit Root Tests: A Fully Bayesian Approach

Diniz

Pereira

Stern³

2020

Entropy

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An extended Hilbert transform method for reconstructing the phase from an oscillatory signal

Matsuki

Kori

Kobayashi

2023

Sci Rep

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Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed signals. A popular method of phase reconstruction is based on the Hilbert transform, which can only reconstruct the interpretable phase from a limited class of signals, e.g., narrow band signals. To address this issue, we propose an extended Hilbert transform method that accurately reconstructs the phase from various oscillatory signals. The proposed method is developed by analyzing the reconstruction error of the Hilbert transform method with the aid of Bedrosian’s theorem. We validate the proposed method using synthetic data and show its systematically improved performance compared with the conventional Hilbert transform method with respect to accurately reconstructing the phase. Finally, we demonstrate that the proposed method is potentially useful for detecting the phase shift in an observed signal. The proposed method is expected to facilitate the study of synchronization phenomena from experimental data.

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Classification of brain states that predicts future performance in visual tasks based on co-integration analysis of EEG data

2022

Self Cite

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Electroencephalogram (EEG) is a popular tool for studying brain activity. Numerous statistical techniques exist to enhance understanding of the complex dynamics underlying the EEG recordings. Inferring the functional network connectivity between EEG channels is of interest, and non-parametric inference methods are typically applied. We propose a fully parametric model-based approach via cointegration analysis. It not only estimates the network but also provides further insight through cointegration vectors, which characterize equilibrium states, and the corresponding loadings, which describe the mechanism of how the EEG dynamics is drawn to the equilibrium. We outline the estimation procedure in the context of EEG data, which faces specific challenges compared with the common econometric problems, for which cointegration analysis was originally conceived. In particular, the dimension is higher, typically around 64; there is usually access to repeated trials; and the data are artificially linearly dependent through the normalization done in EEG recordings. Finally, we illustrate the method on EEG data from a visual task experiment and show how brain states identified via cointegration analysis can be utilized in further investigations of determinants playing roles in sensory identifications.

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Oscillating systems with cointegrated phase processes

Cited by 8 publications

References 30 publications

Cointegration and Unit Root Tests: A Fully Bayesian Approach

Cointegration and Unit Root Tests: A Fully Bayesian Approach

An extended Hilbert transform method for reconstructing the phase from an oscillatory signal

Classification of brain states that predicts future performance in visual tasks based on co-integration analysis of EEG data

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