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Single‐Index Additive Vector Autoregressive Time Series Models

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  • YEHUA LI
  • MARC G. GENTON

Abstract

. We study a new class of nonlinear autoregressive models for vector time series, where the current vector depends on single‐indexes defined on the past lags and the effects of different lags have an additive form. A sufficient condition is provided for stationarity of such models. We also study estimation of the proposed model using P‐splines, hypothesis testing, asymptotics, selection of the order of the autoregression and of the smoothing parameters and nonlinear forecasting. We perform simulation experiments to evaluate our model in various settings. We illustrate our methodology on a climate data set and show that our model provides more accurate yearly forecasts of the El Niño phenomenon, the unusual warming of water in the Pacific Ocean.

Suggested Citation

  • Yehua Li & Marc G. Genton, 2009. "Single‐Index Additive Vector Autoregressive Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 369-388, September.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:3:p:369-388
    DOI: 10.1111/j.1467-9469.2009.00641.x
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    References listed on IDEAS

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    1. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534, December.
    2. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    3. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    4. Philippe C. Besse & Herve Cardot & David B. Stephenson, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687, December.
    5. Annie Qu & Runze Li, 2006. "Quadratic Inference Functions for Varying-Coefficient Models with Longitudinal Data," Biometrics, The International Biometric Society, vol. 62(2), pages 379-391, June.
    6. 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:

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    2. Siti Mariam Norrulashikin, 2015. "An Investigation Towards The Suitability Of Vector Autoregressive Approach On Modeling Meteorological Data," Modern Applied Science, Canadian Center of Science and Education, vol. 9(11), pages 1-89, October.
    3. Liao, Jun & Zong, Xianpeng & Zhang, Xinyu & Zou, Guohua, 2019. "Model averaging based on leave-subject-out cross-validation for vector autoregressions," Journal of Econometrics, Elsevier, vol. 209(1), pages 35-60.
    4. Tracy Wu & Haiqun Lin & Yan Yu, 2011. "Single-index coefficient models for nonlinear time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 37-58.
    5. Gonçalves, Carla & Bessa, Ricardo J. & Pinson, Pierre, 2021. "A critical overview of privacy-preserving approaches for collaborative forecasting," International Journal of Forecasting, Elsevier, vol. 37(1), pages 322-342.
    6. Binglin Li & Hao Xu & Yufeng Lian & Pai Li & Yong Shao & Chunyu Tan, 2023. "An Empirical Modal Decomposition-Improved Whale Optimization Algorithm-Long Short-Term Memory Hybrid Model for Monitoring and Predicting Water Quality Parameters," Sustainability, MDPI, vol. 15(24), pages 1-18, December.

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