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Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR–ARCH type processes

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  • Ziel, Florian

Abstract

Shrinkage algorithms are of great importance in almost every area of statistics due to the increasing impact of big data. Especially time series analysis benefits from efficient and rapid estimation techniques such as the lasso. However, currently lasso type estimators for autoregressive time series models still focus on models with homoscedastic residuals. Therefore, an iteratively reweighted adaptive lasso algorithm for the estimation of time series models under conditional heteroscedasticity is presented in a high-dimensional setting. The asymptotic behaviour of the resulting estimator is analysed. It is found that the proposed estimation procedure performs substantially better than its homoscedastic counterpart. A special case of the algorithm is suitable to compute the estimated multivariate AR–ARCH type models efficiently. Extensions to the model like periodic AR–ARCH, threshold AR–ARCH or ARMA–GARCH are discussed. Finally, different simulation results and applications to electricity market data and returns of metal prices are shown.

Suggested Citation

  • Ziel, Florian, 2016. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR–ARCH type processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 773-793.
    • Handle: RePEc:eee:csdana:v:100:y:2016:i:c:p:773-793
    DOI: 10.1016/j.csda.2015.11.016
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    Cited by:

    1. Simon Hirsch & Jonathan Berrisch & Florian Ziel, 2024. "Online Distributional Regression," Papers 2407.08750, arXiv.org, revised Aug 2024.
    2. Bartosz Uniejewski & Jakub Nowotarski & Rafał Weron, 2016. "Automated Variable Selection and Shrinkage for Day-Ahead Electricity Price Forecasting," Energies, MDPI, vol. 9(8), pages 1-22, August.
    3. Jiajia Li & Yucong Liu & Houjian Li & Abbas Ali Chandio, 2021. "Heterogeneous Driving Factors of Carbon Emissions Embedded in China’s Export: An Application of the LASSO Model," IJERPH, MDPI, vol. 18(19), pages 1-18, October.
    4. Florian Ziel & Rafal Weron, 2016. "Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate models," HSC Research Reports HSC/16/08, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    5. Ziel, Florian & Steinert, Rick, 2016. "Electricity price forecasting using sale and purchase curves: The X-Model," Energy Economics, Elsevier, vol. 59(C), pages 435-454.
    6. Rostami-Tabar, Bahman & Ziel, Florian, 2022. "Anticipating special events in Emergency Department forecasting," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1197-1213.
    7. Smeekes, Stephan & Wijler, Etienne, 2018. "Macroeconomic forecasting using penalized regression methods," International Journal of Forecasting, Elsevier, vol. 34(3), pages 408-430.
    8. Bartosz Uniejewski, 2024. "Regularization for electricity price forecasting," Papers 2404.03968, arXiv.org.
    9. Jens Kley-Holsteg & Florian Ziel, 2020. "Probabilistic Multi-Step-Ahead Short-Term Water Demand Forecasting with Lasso," Papers 2005.04522, arXiv.org.
    10. Ambach, Daniel & Schmid, Wolfgang, 2017. "A new high-dimensional time series approach for wind speed, wind direction and air pressure forecasting," Energy, Elsevier, vol. 135(C), pages 833-850.
    11. Ziel, Florian & Weron, Rafał, 2018. "Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks," Energy Economics, Elsevier, vol. 70(C), pages 396-420.
    12. Aknouche, Abdelhakim & Al-Eid, Eid & Demouche, Nacer, 2016. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," MPRA Paper 75770, University Library of Munich, Germany, revised 19 Dec 2016.
    13. Abdelhakim Aknouche & Eid Al-Eid & Nacer Demouche, 2018. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," Statistical Inference for Stochastic Processes, Springer, vol. 21(3), pages 485-511, October.

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