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Experimental Methods to Study Human Postural Control
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Published on: September 11, 2019

Nonparametric Transfer Function Models.

Jun M Liu1, Rong Chen, Qiwei Yao

  • 1Jun M. Liu is Assistant Professor of Quantitative Methods, Department of Finance & Quantitative Analysis, Georgia Southern University.

Journal of Econometrics
|July 15, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces novel nonparametric transfer function models for nonlinear time series. These models efficiently estimate unknown transfer functions and autoregressive-moving average (ARMA) noise parameters simultaneously.

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Area of Science:

  • Time Series Analysis
  • Nonparametric Statistics
  • Econometrics

Background:

  • Modeling nonlinear relationships between input and output time series is crucial in various scientific domains.
  • Existing methods often struggle with unknown functional forms and correlated noise structures.

Purpose of the Study:

  • To propose a class of nonparametric transfer function models for nonlinear time series.
  • To jointly estimate the smooth, unknown transfer function and the stationary autoregressive-moving average (ARMA) noise parameters.
  • To enhance estimation efficiency by modeling noise correlation and utilizing parsimonious ARMA structures.

Main Methods:

  • Development of a joint estimation procedure for nonparametric transfer functions and ARMA parameters.
  • Leveraging the properties of stationary autoregressive-moving average (ARMA) processes for noise modeling.
  • Asymptotic analysis of the proposed estimators.

Main Results:

  • The proposed method allows for efficient estimation of the nonparametric transfer function by accounting for autocorrelation in the noise.
  • The inclusion of a parsimonious ARMA structure improves estimation efficiency, particularly in finite sample scenarios.
  • Simulation studies and an empirical example demonstrate the practical utility and performance of the developed models.

Conclusions:

  • The proposed nonparametric transfer function models provide a flexible and efficient approach for analyzing nonlinear time series with correlated noise.
  • Joint estimation of the transfer function and ARMA parameters leads to improved statistical properties.
  • The methodology is validated through theoretical analysis and empirical application.