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Estimating linear dependence between nonstationary time series using the locally stationary wavelet model

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  • J. Sanderson
  • P. Fryzlewicz
  • M. W. Jones

Abstract

Large volumes of neuroscience data comprise multiple, nonstationary electrophysiological or neuroimaging time series recorded from different brain regions. Accurately estimating the dependence between such neural time series is critical, since changes in the dependence structure are presumed to reflect functional interactions between neuronal populations. We propose a new dependence measure, derived from a bivariate locally stationary wavelet time series model. Since wavelets are localized in both time and scale, this approach leads to a natural, local and multi-scale estimate of nonstationary dependence. Our methodology is illustrated by application to a simulated example, and to electrophysiological data relating to interactions between the rat hippocampus and prefrontal cortex during working memory and decision making. Copyright 2010, Oxford University Press.

Suggested Citation

  • J. Sanderson & P. Fryzlewicz & M. W. Jones, 2010. "Estimating linear dependence between nonstationary time series using the locally stationary wavelet model," Biometrika, Biometrika Trust, vol. 97(2), pages 435-446.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:2:p:435-446
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    File URL: http://hdl.handle.net/10.1093/biomet/asq007
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    Cited by:

    1. Guy Nason, 2013. "A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 879-904, November.
    2. Wang, Jiangyan & Cao, Guanqun & Wang, Li & Yang, Lijian, 2020. "Simultaneous confidence band for stationary covariance function of dense functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    3. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Euan T. McGonigle & Rebecca Killick & Matthew A. Nunes, 2022. "Trend locally stationary wavelet processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 895-917, November.
    5. Aykroyd, Robert G. & Barber, Stuart & Miller, Luke R., 2016. "Classification of multiple time signals using localized frequency characteristics applied to industrial process monitoring," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 351-362.
    6. Embleton, Jonathan & Knight, Marina I. & Ombao, Hernando, 2022. "Wavelet testing for a replicate-effect within an ordered multiple-trial experiment," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    7. Milan Bašta, 2014. "Simulating Bivariate Stationary Processes with Scale-Specific Characteristics," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2014(1), pages 3-26.
    8. Mark Fiecas & Hernando Ombao, 2016. "Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1440-1453, October.
    9. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.

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