Non parametric functional predictive model in functional time series. Application in meteorological variables.
DOI:
https://doi.org/10.47187/perf.v1i28.186Keywords:
Functional nonparametric model, functional time series, meteorological variables, wind speedAbstract
The research starts from the study of the non-parametric functional model for functional time series. The objective is to establish predictions of functional time series that are formed with the sample of the average wind speeds in each hour of the months of January to December of the year 2019. The sample was taken from the meteorological station of the Escuela Superior Politécnica de Chimborazo located in the San Juan Parish at 4350 meters above sea level at the 30th kilometer of the Calpi - Guaranda road in the province of Chimborazo - Ecuador. The fda,usc package of the R software was used for the application of the functional time series in the aforementioned model, then with this model the adjustments were obtained, the optimal window width typical of a non-parametric model, the predictions of the Time series of 24 values corresponding to each hour in the interval from 0:00 to 23:00, very close to the series of wind speeds for the month of December taken as the control month. This sets the standard to testify that the adjusted model in this research is significantly reliable, and opens the way for future applications in other meteorological variables.
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Aneiros-Pérez G, Cao R, Vilar-Fernández JM. Functional methods for time series prediction: a nonparametric approach. J Forecast [Internet]. 2011;30(4):377–92. Available from: https://www.eco.uc3m.es/temp/Cao%202.pdf
Aneiros G, Vilar JM, Cao R, Munoz San Roque A. Functional prediction for the residual demand in electricity spot markets. IEEE Trans Power Syst [Internet]. 2013 [cited 2022 Dec 12];28(4):4201–8. Available from: https://www.iit.comillas.edu/docs/IIT-13-164A-Preview.pdf
Aneiros-Pérez G, Cardot H, Estévez-Pérez G, Vieu P. Maximum ozone concentration forecasting by functional non-parametric approaches: MAXIMUM OZONE CONCENTRATION FORECASTING. Environmetrics [Internet]. 2004;15(7):675–85. Available from: http://dx.doi.org/10.1002/env.659
Berlinet, A. and Levallois, S. Higher order analysis at Lebesgue points. In: Puri, M. (Ed.), Asymptotics in Statistics and Probability, 2001. VSP
Beyaztas U, Shang HL. On function-on-function regression: Partial least squares approach [Internet]. arXiv [stat.ME]. 2019 [cited 2022 Dec 12]. Available from: https://pubag.nal.usda.gov/catalog/6848647
De Boor C. A practical guide to splines. 1st ed. New York, NY: Springer; 2001.
Bosq D. Nonparametric statistics for stochastic processes: Estimation and prediction [Internet]. 2nd ed. New York, NY: Springer; 1998. Available from: https://books.google.at/books?id=tZDqBwAAQBAJ
Bosq D. Linear processes in function spaces: Theory and applications. New York, NY: Springer; 2000.
Cuevas A, Febrero M, Fraiman R. Linear functional regression: The case of fixed design and functional response. Can J Stat [Internet]. 2002;30(2):285–300. Available from: http://dx.doi.org/10.2307/3315952
Damon J, Guillas S. Estimation and simulation of autoregressive hilbertian processes with exogenous variables. Stat Inference Stoch Process [Internet]. 2005;8(2):185–204. Available from: http://dx.doi.org/10.1007/s11203-004-1031-6
Damon J, Guillas S. The inclusion of exogenous variables in functional autoregressive ozone forecasting. Environmetrics [Internet]. 2002;13(7):759–74. Available from: http://dx.doi.org/10.1002/env.527
Febrero-Bande M, de la Fuente MO. Statistical Computing in Functional Data Analysis: The R Package fda.Usc. J Stat Softw [Internet]. 2012 [cited 2022 Dec 12];51(4). Available from: https://www.academia.edu/22388623/Statistical_Computing_in_Functional_Data_Analysis_The_R_Package_fda_usc
Febrero-Bande M, Galeano P, González-Manteiga W. Functional principal component regression and functional partial least-squares regression: An overview and a comparative study. Int Stat Rev [Internet]. 2017;85(1):61–83. Available from: http://dx.doi.org/10.1111/insr.12116
Ferraty, F. Estimation non-paramétrique et discrimination de courbes. Proceedings of SFC 2001 Conference, Guadeloupe, 2001;17–21.
Ferraty F, Goia A, Vieu P. Functional nonparametric model for time series: a fractal approach for dimension reduction. Test (Madr) [Internet]. 2002;11(2):317–44. Available from: http://dx.doi.org/10.1007/bf02595710
Ferraty F, Vieu P. The functional nonparametric model and application to spectrometric data. Comput Stat [Internet]. 2002;17(4):545–64. Available from: http://dx.doi.org/10.1007/s001800200126
Ferraty F, Vieu P. Curves discrimination: a nonparametric functional approach. Comput Stat Data Anal [Internet]. 2003;44(1–2):161–73. Available from: https://www.sciencedirect.com/science/article/pii/S016794730300032X
Ferraty F, Mas A, Vieu P. Nonparametric regression on functional data: inference and practical aspects. Aust. N.Z.J. Stat. 2007; 49:267-286. Available from: https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-842X.2007.00480.x
Ferraty F, Van Keilegom I, Vieu P. On the Validity of the Bootstrap in Non-Parametric Functional Regression: Bootstrap in functional regression. Scand Stat Theory Appl [Internet]. 2009;37(2):286–306. Available from: http://dx.doi.org/10.1111/j.1467-9469.2009.00662.x
Ferraty F, Vieu P. Nonparametric Functional Data Analysis. (2006). Springer.
Horváth L, Kokoszka P. Inference for functional data with applications [Internet]. 2012th ed. New York, NY: Springer; 2012. Available from: https://books.google.at/books?id=OVezLB__ZpYC
Peña D. Análisis de series temporales [Internet]. Alianzaeditorial.es. [cited 2022 Dec 12]. Available from: https://www.alianzaeditorial.es/libro/manuales/analisis-de-series-temporales-daniel-pena-9788420669458/
Portela González J. Functional time series forecasting in electricity markets : a novel parametric approach. 2017.
Silverman BW, Ramsay JO. Applied functional data analysis: Methods and case studies. 2002 [cited 2022 Dec 12]; Available from: https://research-information.bris.ac.uk/en/publications/applied-functional-data-analysis-methods-and-case-studies
Ramsay, J.o. and Silverman, B.w. (2005) Functional Data Analysis. Springer, New York. - references - scientific research publishing [Internet]. Scirp.org. [cited 2022 Dec 12]. Available from: https://www.scirp.org/(S(lz5mqp453edsnp55rrgjct55))/reference/referencespapers.aspx?referenceid=2016706
M. G. schimek, “Smoothing and Regression Approaches, Computation, and Application,” Wiley Series in Probability and Statistics Applied Probability and Statistics Section, Wiley, New York, 2000. - references - scientific research publishing [Internet]. Scirp.org. [cited 2022 Dec 12]. Available from: https://www.scirp.org/(S(czeh2tfqw2orz553k1w0r45))/reference/referencespapers.aspx?referenceid=1047228
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