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Dimension reduction for the conditional mean and variance functions in time series

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  • Jin‐Hong Park
  • S. Yaser Samadi

Abstract

This paper deals with the nonparametric estimation of the mean and variance functions of univariate time series data. We propose a nonparametric dimension reduction technique for both mean and variance functions of time series. This method does not require any model specification and instead we seek directions in both the mean and variance functions such that the conditional distribution of the current observation given the vector of past observations is the same as that of the current observation given a few linear combinations of the past observations without loss of inferential information. The directions of the mean and variance functions are estimated by maximizing the Kullback–Leibler distance function. The consistency of the proposed estimators is established. A computational procedure is introduced to detect lags of the conditional mean and variance functions in practice. Numerical examples and simulation studies are performed to illustrate and evaluate the performance of the proposed estimators.

Suggested Citation

  • Jin‐Hong Park & S. Yaser Samadi, 2020. "Dimension reduction for the conditional mean and variance functions in time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(1), pages 134-155, March.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:1:p:134-155
    DOI: 10.1111/sjos.12405
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    Cited by:

    1. Tharindu P. De Alwis & S. Yaser Samadi, 2024. "Stacking-based neural network for nonlinear time series analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(3), pages 901-924, July.
    2. da Silva, Murilo & Sriram, T.N. & Ke, Yuan, 2023. "Dimension reduction in time series under the presence of conditional heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    3. S. Yaser Samadi & Tharindu P. De Alwis, 2023. "Fourier Methods for Sufficient Dimension Reduction in Time Series," Papers 2312.02110, arXiv.org.

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