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Time series clustering based on forecast densities. (English) Zbl 1157.62484
Summary: A new clustering method for time series is proposed, based on the full probability density of the forecasts. First, a resampling method combined with a nonparametric kernel estimator provides estimates of the forecast densities. A measure of discrepancy is then defined between these estimates and the resulting dissimilarity matrix is used to carry out the required cluster analysis. Applications of this method to both simulated and real life data sets are discussed.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
62G07 Density estimation
62H30 Classification and discrimination; cluster analysis (statistical aspects)
Software:
TRAMO
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[1] Alonso, A.M.; Peña, D.; Romo, J., Forecasting time series with sieve bootstrap, J. statist. plann. inference, 100, 1-11, (2002) · Zbl 1007.62077
[2] Alonso, A.M.; Peña, D.; Romo, J., On sieve bootstrap prediction intervals, Statist. probab. lett., 65, 13-20, (2003) · Zbl 1048.62049
[3] Bickel, P.J.; Bühlmann, P., A new mixing notion and functional central limits theorems for a sieve bootstrap in time series, Bernoulli, 5, 413-446, (1999) · Zbl 0954.62102
[4] Box, G.; Jenkins, G.M.; Reinsel, G., Time series analysis: forecasting and control, (1994), Prentice-Hall Englewood Cliffs · Zbl 0858.62072
[5] Cao, R.; Febrero-Bande, M.; González-Manteiga, W.; Prada-Sánchez, J.M.; García-Jurado, I., Saving computer time in constructing consistent bootstrap prediction intervals for autoregressive processes, Comm. statist. simulation comput., 26, 961-978, (1997) · Zbl 0925.62395
[6] Cowpertwait, P.S.P.; Cox, T.F., Clustering population means under heterogeneity of variance with an application to a rainfall time series problem, The Statistician, 41, 113-121, (1992)
[7] Everitt, B.S.; Landau, S.; Leese, M., Cluster analysis, (2001), Arnold London · Zbl 1205.62076
[8] Fruhwirth-Schnatter, S., Kaufmann, S., 2004. Model-based clustering of multiple time series. CEPR Discussion Paper No. 4650. · Zbl 1091.62076
[9] Galeano, P.; Peña, D., Multivariate analysis in vector time series, Resenhas, 4, 383-403, (2000) · Zbl 1098.62558
[10] Gómez, V.; Maravall, A., Estimation, prediction, and interpolation for nonstationary series with the Kalman filter, J. amer. statist. assoc., 89, 611-624, (1994) · Zbl 0806.62076
[11] Gómez, V., Maravall, A., 1996. Programs TRAMO (Time Series Regression with ARIMA noise, Missing observations and Outliers) and SEATS (Signal Extraction in ARIMA Time Series). Instruction for the user. Working Paper 9628, Bank of Spain, Madrid.
[12] Gómez, V., Maravall, A., 2001. Automatic modeling methods for univariate series. In: Peña, D., Tiao, G.C., Tsay, R.S. (Eds.), A Course in Time Series, Wiley, New York (Chapter 7).
[13] Hannan, E.J.; Deistler, M., The statistical theory of linear systems, (1988), Wiley New York · Zbl 0641.93002
[14] Hannan, E.J.; Kavalieris, L., Regression, autoregression models, J. time ser. anal., 7, 27-49, (1986) · Zbl 0588.62163
[15] Hurvich, C.M.; Tsai, C.-L., Regression and time series model selection in small samples, Biometrika, 76, 297-307, (1989) · Zbl 0669.62085
[16] Kakizawa, Y.; Shumway, R.H.; Taniguchi, M., Discrimination and clustering for multivariate time series, J. amer. statist. assoc., 93, 328-340, (1998) · Zbl 0906.62060
[17] Macchiato, M.F.; La Rotonda, L.; Lapenna, V.; Ragosta, M., Time modelling and spatial clustering of daily ambient temperature: an application in southern Italy, Environmetrics, 6, 31-53, (1995)
[18] Maharaj, E.A., A significance test for classifying ARMA models, J. statist. comput. simulation, 54, 305-331, (1996) · Zbl 0899.62116
[19] Pascual, L.; Romo, J.; Ruiz, E., Bootstrap predictive inference for ARIMA processes, J. time ser. anal., 25, 449-465, (2004) · Zbl 1062.62199
[20] Pattarin, F.; Paterlini, S.; Minerva, T., Clustering financial time series: an application to mutual funds style analysis, Comput. statist. data anal., 47, 353-372, (2004) · Zbl 1429.62476
[21] Phillips, P.C.B.; Solo, V., Asymptotics for linear processes, Ann. statist., 20, 971-1001, (1992) · Zbl 0759.60021
[22] Piccolo, D., A distance measure for classifying ARIMA models, J. time ser. anal., 11, 153-164, (1990) · Zbl 0691.62083
[23] Sheather, S.J.; Hettmansperger, T.P.; Donald, M.R., Data – based bandwidth selection for kernel estimators of the integral of \(f^2(x)\), Scand. J. statist., 21, 265-275, (1994) · Zbl 0802.62043
[24] Silverman, B.W., Density estimation for statistics and data analysis, (1986), Chapman & Hall London · Zbl 0617.62042
[25] Thombs, L.A.; Schucany, W.R., Bootstrap prediction intervals for autoregression, J. amer. statist. assoc., 85, 486-492, (1990) · Zbl 0705.62089
[26] United Nations, 1997. Kyoto Protocol to the United Nations Framework Convention on Climate Change. New York.
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