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Extracting Conditionally Heteroskedastic Components using Independent Component Analysis.

ABSTRACT: In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In this article, we study an ICA method which combines the use of linear and quadratic autocorrelations to enable efficient estimation of various kinds of stationary time series. Statistical properties of the estimator are studied by finding its limiting distribution under general conditions, and the asymptotic variances are derived in the case of ARMA-GARCH model. We use the asymptotic results and a finite sample simulation study to compare different choices of a weight coefficient. As it is often of interest to identify all those components which exhibit stochastic volatility features we suggest a test statistic for this problem. We also show that a slightly modified version of the principal volatility component analysis can be seen as an ICA method. Finally, we apply the estimators in analysing a data set which consists of time series of exchange rates of seven currencies to US dollar. Supporting information including proofs of the theorems is available online.

SUBMITTER: Miettinen J

PROVIDER: S-EPMC7266430 | biostudies-literature | 2020 Mar

REPOSITORIES: biostudies-literature

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Extracting Conditionally Heteroskedastic Components using Independent Component Analysis.

Miettinen Jari J Matilainen Markus M Nordhausen Klaus K Taskinen Sara S

Journal of time series analysis 20190908 2

In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In this article, we study an ICA method which combines the use of linear and quadratic autocorrelations to enable efficient estimation of various kinds of stationary time series. Statistical properties of the estimator are studied by finding its limiting distribution under general ...[more]

PMID: 32508370

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Project description:The success of stereoelectroencephalographic (SEEG) investigations depends crucially on the hypotheses on the putative location of the seizure onset zone. This information is derived from non-invasive data either based on visual analysis or advanced source localization algorithms. While source localization applied to interictal spikes recorded on scalp is the classical method, it does not provide unequivocal information regarding the seizure onset zone. Raw ictal activity contains a mixture of signals originating from several regions of the brain as well as EMG artifacts, hampering direct input to the source localization algorithms. We therefore introduce a methodology that disentangles the various sources contributing to the scalp ictal activity using independent component analysis and uses equivalent current dipole localization as putative locus of ictal sources. We validated the results of our analysis pipeline by performing long-term simultaneous scalp - intracerebral (SEEG) recordings in 14 patients and analyzing the wavelet coherence between the independent component encoding the ictal discharge and the SEEG signals in 8 patients passing the inclusion criteria. Our results show that invasively recorded ictal onset patterns, including low-voltage fast activity, can be captured by the independent component analysis of scalp EEG. The visibility of the ictal activity strongly depends on the depth of the sources. The equivalent current dipole localization can point to the seizure onset zone (SOZ) with an accuracy that can be as high as 10 mm for superficially located sources, that gradually decreases for deeper seizure generators, averaging at 47 mm in the 8 analyzed patients. Independent component analysis is therefore shown to have a promising SOZ localizing value, indicating whether the seizure onset zone is neocortical, and its approximate location, or located in mesial structures. That may contribute to a better crafting of the hypotheses used as basis of the stereo-EEG implantations.

Dataset Information

Extracting Conditionally Heteroskedastic Components using Independent Component Analysis.

Publications

Extracting Conditionally Heteroskedastic Components using Independent Component Analysis.

Similar Datasets

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