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A functional linear model for time series prediction with exogenous variables

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  • Goia, Aldo

Abstract

This note deals with the study of a functional linear model for time series prediction which combines a functional endogenous predictor and real and functional exogenous variables. A penalized B-spline type estimator for the real and functional coefficients is presented and some weak consistency results are derived under suitable conditions.

Suggested Citation

  • Goia, Aldo, 2012. "A functional linear model for time series prediction with exogenous variables," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1005-1011.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:1005-1011
    DOI: 10.1016/j.spl.2012.02.009
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    References listed on IDEAS

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    1. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    2. Germán Aneiros‐Pérez & Ricardo Cao & Juan M. Vilar‐Fernández, 2011. "Functional methods for time series prediction: a nonparametric approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(4), pages 377-392, July.
    3. Frédéric Ferraty & Aldo Goia & Philippe Vieu, 2002. "Functional nonparametric model for time series: a fractal approach for dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 317-344, December.
    4. Goia, Aldo & May, Caterina & Fusai, Gianluca, 2010. "Functional clustering and linear regression for peak load forecasting," International Journal of Forecasting, Elsevier, vol. 26(4), pages 700-711, October.
    5. Jaromir Antoch & Lubos Prchal & Maria Rosaria De Rosa & Pascal Sarda, 2010. "Electricity consumption prediction with functional linear regression using spline estimators," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(12), pages 2027-2041.
    6. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    7. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601, December.
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    Cited by:

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    2. Usset, Joseph & Staicu, Ana-Maria & Maity, Arnab, 2016. "Interaction models for functional regression," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 317-329.
    3. Maeng, Hye Young & Fryzlewicz, Piotr, 2019. "Regularised forecasting via smooth-rough partitioning of the regression coefficients," LSE Research Online Documents on Economics 100878, London School of Economics and Political Science, LSE Library.
    4. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
    5. Manuel Febrero-Bande & Wenceslao González-Manteiga, 2013. "Generalized additive models for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 278-292, June.
    6. Pedro Delicado & Philippe Vieu, 2017. "Choosing the most relevant level sets for depicting a sample of densities," Computational Statistics, Springer, vol. 32(3), pages 1083-1113, September.
    7. Bongiorno, Enea G. & Goia, Aldo, 2016. "Classification methods for Hilbert data based on surrogate density," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 204-222.

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