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Characterization of the partial autocorrelation function of nonstationary time series

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  • Dégerine, Serge
  • Lambert-Lacroix, Sophie

Abstract

The second order properties of a process are usually characterized by the autocovariance function. In the stationary case, the parameterization by the partial autocorrelation function is relatively recent. We extend this parameterization to the nonstationary case. The advantage of this function is that it is subject to very simple constraints in comparison with the auto- covariance function which must be nonnegative definite. As in the stationary case, this parameterization is well adapted to autoregressive models or to the identification of deterministic processes.

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  • Dégerine, Serge & Lambert-Lacroix, Sophie, 2003. "Characterization of the partial autocorrelation function of nonstationary time series," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 46-59, October.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:1:p:46-59
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    References listed on IDEAS

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    1. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
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    3. Guoqiang Sun & Tong Chen & Zhinong Wei & Yonghui Sun & Haixiang Zang & Sheng Chen, 2016. "A Carbon Price Forecasting Model Based on Variational Mode Decomposition and Spiking Neural Networks," Energies, MDPI, vol. 9(1), pages 1-16, January.
    4. Jianguo Zhou & Xuejing Huo & Xiaolei Xu & Yushuo Li, 2019. "Forecasting the Carbon Price Using Extreme-Point Symmetric Mode Decomposition and Extreme Learning Machine Optimized by the Grey Wolf Optimizer Algorithm," Energies, MDPI, vol. 12(5), pages 1-22, March.
    5. Jianguo Zhou & Qiqi Wang, 2021. "Forecasting Carbon Price with Secondary Decomposition Algorithm and Optimized Extreme Learning Machine," Sustainability, MDPI, vol. 13(15), pages 1-17, July.
    6. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.

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