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Spline confidence bands for variance functions in nonparametric time series regressive models

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  • Yujiao Yang
  • Yuhang Xu
  • Qiongxia Song

Abstract

For nonparametric time series regression, we propose to apply polynomial splines to squared residuals to develop the variance function estimation. Furthermore, we obtain and use simultaneous confidence bands to detect certain parametric forms for entire variance curves. The proposed method is extremely fast. Asymptotic results are established under the assumption that observations are from a strictly stationary $\alpha$-mixing process. Simulations and a financial data set application are provided to illustrate the performance of the proposed method numerically.

Suggested Citation

  • Yujiao Yang & Yuhang Xu & Qiongxia Song, 2012. "Spline confidence bands for variance functions in nonparametric time series regressive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 699-714.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:699-714
    DOI: 10.1080/10485252.2012.693925
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    References listed on IDEAS

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    1. Francesco Audrino & Peter Bühlmann, 2009. "Splines for financial volatility," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 655-670, June.
    2. Qiongxia Song & Lijian Yang, 2009. "Spline confidence bands for variance functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 589-609.
    3. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    4. Li Wang & Lijian Yang, 2010. "Simultaneous confidence bands for time-series prediction function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 999-1018.
    5. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    6. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    7. Jianhua Z. Huang & Lijian Yang, 2004. "Identification of non‐linear additive autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 463-477, May.
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    Cited by:

    1. Shao, Zhen & Gao, Fei & Yang, Shan-Lin & Yu, Ben-gong, 2015. "A new semiparametric and EEMD based framework for mid-term electricity demand forecasting in China: Hidden characteristic extraction and probability density prediction," Renewable and Sustainable Energy Reviews, Elsevier, vol. 52(C), pages 876-889.

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