Using robust FPCA to identify outliers in functional time series, with applications to the electricity market

Juan Manuel Vilar Fernández; Paula Raña Míguez; Germán Aneiros Pérez

Ayuda

Using robust FPCA to identify outliers in functional time series, with applications to the electricity market

Juan M.Vilar ^[1] ; Paula Raña ^[1] ; Germán Aneiros ^[1]
1. [1] Universidade da Coruña
  
  Universidade da Coruña
  
  A Coruña, España
Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 40, Nº. 2, 2016, págs. 321-348
Idioma: inglés
Enlaces
- Texto completo (pdf)
Resumen
- This study proposes two methods for detecting outliers in functional time series. Both methods take dependence in the data into account and are based on robust functional principal component analysis. One method seeks outliers in the series of projections on the first principal component. The other obtains uncontaminated forecasts for each data set and determines that those observations whose residuals have an unusually high norm are considered outliers. A simulation study shows the performance of these proposed procedures and the need to take dependence in the time series into account. Finally, the usefulness of our methodology is illustrated in two real datasets from the electricity market: daily curves of electricity demand and price in mainland Spain, for the year 2012.
Referencias bibliográficas
- Aneiros-PeÌrez, G., Cardot, H, EsteÌvez-Perez, G., and Vieu, P. (2004). Maximum ozone concentration forecasting by functional non-parametric...
- Aneiros, G., Vilar, J.M., Cao, R., and MunÌoz-San-Roque, A. (2013). Functional prediction for the residual demand in electricity spot markets....
- Aneiros, G., Vilar, J., and RanÌa, P. (2016). Short-term forecast of daily curves of electricity demand and price. Electrical Power and Energy...
- Antoch, J., Prchal, L., De Rosa, M.R., and Sarda, P. (2010). Electricity consumption prediction with functional linear regression using spline...
- Antoniadis, A., Paparoditis, E., and Sapatinas, T. (2006). A functional wavelet kernel approach for time series prediction. Journal of the...
- Arribas-Gil, A., and Romo, J. (2014). Shape outlier detection and visualization for functional data: the outliergram. Biostatistics, 15, 603–619.
- BaÄ±Ìllo, A., Cuesta-Albertos, J.A., and Cuevas, A. (2011). Supervised classification for a family of Gaussian functional models. Scandinavian...
- Besse, P.C., Cardot, H., and Stephenson, D. (2000). Autoregressive forecasting of some functional climatic variations. Scandinavian Journal...
- Boente, G., and Fraiman, R. (2000). Kernel-based functional principal components. Statistics and Probability Letters, 48, 335–345.
- Cardot, H., Ferraty, F., and Sarda, P. (1999). Functional linear model. Statistics and Probability Letters, 45, 11–22.
- Cho, H., Goude, Y., Brossat, X., and Yao, Q. (2013). Modeling and forecasting daily electricity load curves: a hybrid approach. Journal of...
- Cryer, J.D., and Chan, K.S. (2008). Time Series Analysis, New York: Springer.
- Cuevas, A. (2014). A partial overview of the theory of statistics with functional data. Journal of Statistical Planning and Inference, 147,...
- Cuevas, A., Febrero, M., and Fraiman, R. (2006). On the use of the bootstrap for estimating functions with functional data. Computational...
- Cuevas, A., Febrero, M., and Fraiman, R. (2007). Robust estimation and classification for functional data via projection-based depth notions....
- Delsol, L., Ferraty, F., and Vieu, P. (2011). Structural test in regression on functional variables. Journal of Multivariate Analysis, 102,...
- Febrero, M., Galeano, P., and GonzaÌlez-Manteiga, W. (2007). Functional analysis of NOx levels: location and scale estimation and outlier...
- Febrero, M., Galeano, P., and GonzaÌlez-Manteiga, W. (2008). Outlier detection in functional data by depth measures, with application to...
- Ferraty, F., and Romain,Y. (Eds.) (2011). The Oxford Handbook of Functional Data Analysis, Oxford: Oxford University Press.
- Ferraty, F., van Keilegom, I., and Vieu, P. (2012). Regression when both response and predictor are functions. Journal of Multivariate Analysis,...
- Ferraty, F., and Vieu, P. (2002). The functional nonparametric model and application to spectrometric data. Computational Statistics, 17,...
- Ferraty, F., and Vieu, P. (2006). Nonparametric Functional Data Analysis, New York: Springer-Verlag.
- Fraiman, R., and Svarc, M. (2013). Resistant estimates for high dimensional and functional data based on random projections. Computational...
- GarcÄ±Ìa-PortugueÌs, E., GonzaÌlez-Manteiga, W., and Febrero-Bande, M. (2014). A goodness-of-fit test for the functional linear model with...
- Gervini, D. (2012). Outlier detection and trimmed estimation for general functional data. Statistica Sinica, 22, 1639–1660.
- GonzaÌlez-Manteiga, W., and MartÄ±Ìnez-Calvo, A. (2011). Bootstrap in functional linear regression. Journal of Statistical Planning and...
- Hall, P. (2011). Principal component analysis for functional data: methodology, theory, and discussion. The Oxford Handbook of Functional...
- Hall, P., MuÌller, H.G., and Wang, J.L. (2006). Properties of principal component methods for functional and longitudinal data analysis....
- HorvaÌth, L., and Kokoszka, P. (2012). Inference for Functional Data with Applications, NewYork: Springer.
- Hubert, M., Rousseeuw, P.J., and Verboven, S. (2002). A fast method of robust principal components with applications to chemometrics. Chemometrics...
- Hyndman, R.J. (1996). Computing and graphing highest density regions. The American Statistician, 50, 120–126.
- Hyndman, R.J., and Ullah, M.S. (2007). Robust forecasting of mortality and fertility rates: A functional data approach. Computational Statistics...
- Hyndman, R.J., and Booth, H. (2008). Stochastic population forecasts using functional data models for mortality, fertility and migration....
- Hyndman, R.J., and Shang, H.L. (2010). Rainbow plots, bagplots, and boxplots for functional data. Journal of Computational and Graphical Statistics,...
- KuÌnsch, H.R. (1989). The jacknife and the bootstrap for general stationary observations. Annals of Statistics, 17, 1217–1241.
- Li, Y., and Hsing, T. (2007). On rates of convergence in functional linear regression. Journal of Multivariate Analysis, 98, 1782–1804.
- Liebl, D. (2013). Modeling and forecasting electricity spot prices: a functional data perspective. Annals of Applied Statistics, 7, 1562–1592.
- OcanÌa, F.A., Aguilera, A.M., and Escabias, M. (2007). Computational considerations in functional principal component analysis. Computational...
- Ramsay, J.O., and Silverman, B.W. (2005). Functional Data Analysis. New York: Springer-Verlag.
- RanÌa, P., Aneiros, G., and Vilar, J.M. (2015). Detection of outliers in functional time series. Environmetrics, 26, 178–191.
- Sawant, P., Billor, N., and Shin, H. (2012). Functional outlier detection with robust functional principal component analysis. Computational...
- Sguera, C., Galeano, P., and Lillo, R. (2014). Spatial depth-based classification for functional data. Test, 23, 725–750.
- Shang, H.L. (2014). Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown...
- Sun, Y., and Genton, M.G. (2011). Functional boxplots. Journal of Computational and Graphical Statistics, 20, 316–334.
- Tsay, R.S., PenÌa, D., and Pankratz, A.E. (2000). Outliers in multivariate time series. Biometrika, 87, 789– 804.
- Vilar, J.M., Cao, R., and Aneiros, G. (2012). Forecasting next-day electricity demand and price using nonparametric functional methods. International...
- Yao, F., MuÌller, H.G., and Wang, J.L. (2005a). Functional linear regression analysis for longitudinal data. Annals of Statistics, 33, 2873–2903.
- Yao, F., MuÌller, H.G., and Wang, J.L. (2005b). Functional data analysis for sparse longitudinal data. Journal of the American Statistical...
- Yu, G., Zou, C., and Wang, Z. (2012). Outlier detection in functional observations with applications to profile monitoring. Technometrics,...