Abstract
When facing any forecasting problem not only is accuracy on the predictions sought. Also, useful information about the underlying physics of the process and about the relevance of the forecasting variables is very much appreciated. In this paper, it is presented an automatic specification procedure for models that are based on additivity assumptions and piecewise linear regression. This procedure allows the analyst to gain insight about the problem by examining the automatically selected model, thus easily checking the validity of the forecast. Monte Carlo simulations have been run to ensure that the model selection procedure behaves correctly under weakly dependent data. Moreover, comparison over other well-known methodologies has been done to evaluate its accuracy performance, both in simulated data and in the context of short-term natural gas demand forecasting. Empirical results show that the accuracy of the proposed model is competitive against more complex methods such as neural networks.
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References
Akaike, H.: Statistical predictor identification. Ann. Inst. Stat. Math. 22(1), 203–217 (1970). doi:10.1007/BF02506337, URL http://www.springerlink.com/content/ch4g3t5064842221/abstract/
Breiman, L., Friedman, J., Stone, C.J., Olshen, R.A.: Classification and Regression Trees, 1st edn. Chapman and Hall, New York (1984)
Chen, R., Tsay, R.S.: Nonlinear additive ARX models. J. Am. Stat. Assoc. 88(423), 955–967 (1993). doi:10.2307/2290787, URL http://www.jstor.org/stable/2290787
Chen, R., Liu, J.S., Tsay, R.S.: Additivity test for nonlinear autoregression. Biometrika 80, 369–383 (1995)
Cheng, B., Tong, H.: On consistent nonparametric order determination and chaos (with discussion). J. R. Stat. Soc. Ser. B Methodol 54, 427–474 (1992)
Clements, M.P., Franses, P.H., Swanson, N.R.: Forecasting economic and financial time-series with non-linear models. Int. J. Forecast. 20(2), 169–183 (2004). doi:10.1016/j.ijforecast.2003.10.004
Cruz, A., Muñoz, A., Luis Zamora, J., Espínola, R.: The effect of wind generation and weekday on spanish electricity spot price forecasting. Electric Power Syst. Res. 81(10), 1924–1935 (2011). doi:10.1016/j.epsr.2011.06.002
Demirel, O.F., Zaim, S., Alikan, A., Zuyar, P.: Forecasting natural gas consumption in Istanbul using neural networks and multivariate time series methods. Turk. J. Electr. Eng. Comput. Sci. 20(5), 695–711 (2012). www.scopus.com
Fan, S., Hyndman, R.J.: Short-term load forecasting based on a semi-parametric additive model. IEEE Trans. Power Syst. 27(1), 134–141 (2012). doi:10.1109/TPWRS.2011.2162082
Friedman, J.H.: A variable span smoother. Tech. rep. (1984) URL http://stinet.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA148241
Gascón, A., Sánchez-Úbeda, E.F.: Application of multi-objective genetic algorithms to fitting piecewise linear models. In: 14th Conference of the Spanish Association for Artificial Intelligence (CAEPIA), Tenerife, Spain (2011)
Guo, Z., Shintani, M.: Nonparametric lag selection for nonlinear additive autoregressive models. Econ. Lett. 111(2), 131–134 (2011). doi:10.1016/j.econlet.2011.01.014
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer, New York (2009)
Huang, J.Z., Yang, L.: Identification of non-linear additive autoregressive models. J. R. Stat. Soc. Ser. B Stat. Methodol. 66(2), 463–477 (2004)
Lewis, P.A.W., Stevens, J.G.: Nonlinear modeling of time series using multivariate adaptive regression splines (MARS). J. Am. Stat. Assoc. 86(416), 864–877 (1991). doi:10.2307/2290499, URL http://www.jstor.org/stable/2290499
Muñoz, A., Czernichow, T.: Variable selection using feedforward and recurrent neural networks. Eng. Intell. Syst. Electr. Eng. Commun. 6(2), 91–102 (1998)
Muñoz, A., Sánchez-Úbeda, E.F., Cruz, A., Marín, J.: Short-term forecasting in power systems: a guided tour. In: Handbook of Power Systems II. Springer, pp. 129–160 (2010)
Pankratz, A.: Forecasting with Dynamic Regression Models. Wiley Series in Probability and Mathematical Statistics, New York, book, Whole (1991)
Sánchez-Úbeda, E.F.: Models for Data Analysis: Contributions to Automatic Learning. PhD thesis, Universidad Pontificia Comillas de Madrid, Madrid, (1999)
Sánchez-Úbeda, E.F., Berzosa, A.: Modeling and forecasting industrial end-use natural gas consumption. Energy Econ. 29(4), 710–742 (2007). doi:10.1016/j.eneco.2007.01.015
Sánchez-Úbeda, E.F., Berzosa, A.: New variables to improve electricity and natural gas consumption forecasting: dynamic degree-days. In: 14th Conference of the Spanish Association for Artificial Intelligence (CAEPIA), Tenerife, Spain (2011)
Sánchez-Úbeda, E.F., Wehenkel, L.: The hinges model: a one-dimensional continuous piecewise polynomial model. In: Proceedings of the International Congress on Information Processing and Management of Uncertainty in Knowledge based Systems, IPMU98, Paris (1998)
Sánchez-Úbeda, E.F., Wehenkel, L.A.: Automatic fuzzy-rules induction by using the ORTHO model. In: Proceedings of Information Processing and Management of Uncertainty in Knowledge-based Systems, Madrid, pp. 1652–1659 (2000)
Soldo, B.: Forecasting natural gas consumption. Appl. Energy 92, 26–37 (2012). doi:10.1016/j.apenergy.2011.11.003
Szoplik, J.: Forecasting of natural gas consumption with artificial neural networks. Energy 85, 208–220 (2015). doi:10.1016/j.energy.2015.03.084, URL http://linkinghub.elsevier.com/retrieve/pii/S036054421500393X
Tjøstheim, D., Auestad, B.H.: Nonparametric identification of nonlinear time series: selecting significant lags. J. Am. Stat. Assoc. 89(428), 1410–1419 (1994). doi:10.2307/2291003, URL http://www.jstor.org/stable/2291003
Tong, H.: Non-Linear Time Series: A Dynamical System Approach. Oxford University Press, Oxford (1993)
Tschernig, R., Yang, L.: Nonparametric lag selection for time series. J. Time Ser. Anal. 21(4), 457–487 (2000). doi:10.1111/1467-9892.00193, URL http://onlinelibrary.wiley.com/doi/10.1111/1467-9892.00193/abstract
Vieu, P.: Order choice in nonlinear autoregressive models. Statistics 26(4), 307–328 (1995). doi:10.1080/02331889508802499, URL http://www.tandfonline.com/doi/abs/10.1080/02331889508802499#preview
Wehenkel, L.A.: Automatic Learning Techniques in Power Systems. Springer, Berlin (1998)
Yang, Y.H.: Can the strengths of AIC and BIC be shared? A conflict between model identification and regression estimation. Biometrika 92(4), 937–950 (2005). doi:10.1093/biomet/92.4.937
Yao, Q., Tong, H.: On subset selection in non-parametric stochastic regression. Stat. Sin. 4(1), 51–70 (1994)
Zhu, L., Li, M.S., Wu, Q.H., Jiang, L.: Short-term natural gas demand prediction based on support vector regression with false neighbours filtered. Energy 80, 428–436 (2015). doi:10.1016/j.energy.2014.11.083, URL http://www.sciencedirect.com/science/article/pii/S0360544214013553
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The authors would like to acknowledge Enagás (Technical Manager of the Spanish gas system) for providing data for the case study.
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Gascón, A., Sánchez-Úbeda, E.F. Automatic specification of piecewise linear additive models: application to forecasting natural gas demand. Stat Comput 28, 201–217 (2018). https://doi.org/10.1007/s11222-017-9726-x
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DOI: https://doi.org/10.1007/s11222-017-9726-x