Statistical analysis for multiplicatively modulated nonlinear autoregressive model and its applications to electrophysiological signal analysis in humans

Hiroko Kato, Masanobu Taniguchi, Manabu Honda

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    Modulating the dynamics of a nonlinear autoregressive model with a radial basis function (RBF) of exogenous variables is known to reduce the prediction error. Here, RBF is a function that decays to zero exponentially if the deviation between the exogenous variables and a center location becomes large. This paper introduces a class of RBF-based multiplicatively modulated nonlinear autoregressive (mmNAR) models. First, we establish the local asymptotic normality (LAN) for vector conditional heteroscedastic autoregressive nonlinear (CHARN) models, which include the mmNAR and many other well-known time-series models as special cases. Asymptotic optimality for estimation and testing is described in terms of LAN properties. The mmNAR model indicates goodness-of-fit for surface electromyograms (EMG) using electrocorticograms (ECoG) as the exogenous variables. Concretely, it is found that the negative potential of the motor cortex forces change in the frequency of EMG, which is reasonable from a physiological point of view. The proposed mmNAR model fitting is both useful and efficient as a signal-processing technique for extracting information on the action potential, which is associated with the postsynaptic potential.

    Original languageEnglish
    Pages (from-to)3414-3425
    Number of pages12
    JournalIEEE Transactions on Signal Processing
    Volume54
    Issue number9
    DOIs
    Publication statusPublished - 2006 Sep

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    Signal analysis
    Statistical methods
    Time series
    Signal processing
    Testing

    Keywords

    • CHARN model
    • Electrocorticogram
    • Electromyogram
    • Local asymptotic normality
    • mmNAR model
    • Radial basis function

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Signal Processing

    Cite this

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    abstract = "Modulating the dynamics of a nonlinear autoregressive model with a radial basis function (RBF) of exogenous variables is known to reduce the prediction error. Here, RBF is a function that decays to zero exponentially if the deviation between the exogenous variables and a center location becomes large. This paper introduces a class of RBF-based multiplicatively modulated nonlinear autoregressive (mmNAR) models. First, we establish the local asymptotic normality (LAN) for vector conditional heteroscedastic autoregressive nonlinear (CHARN) models, which include the mmNAR and many other well-known time-series models as special cases. Asymptotic optimality for estimation and testing is described in terms of LAN properties. The mmNAR model indicates goodness-of-fit for surface electromyograms (EMG) using electrocorticograms (ECoG) as the exogenous variables. Concretely, it is found that the negative potential of the motor cortex forces change in the frequency of EMG, which is reasonable from a physiological point of view. The proposed mmNAR model fitting is both useful and efficient as a signal-processing technique for extracting information on the action potential, which is associated with the postsynaptic potential.",
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    KW - Radial basis function

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