A new robust estimation method for ARMA models

IEEE Transactions on Signal Processing

Volumn 58, Issue 7, 2010, Pages 3512-3522

  Chakhchoukh, Yacine ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

ARMA models; Outliers; Ratio of medians estimator; Robust estimation; Time series

Indexed keywords

ARMA MODEL; ASYMPTOTIC VARIANCE; AUTO REGRESSIVE MODELS; AUTOCORRELATION FUNCTIONS; AUTOREGRESSIVE MOVING AVERAGE; BREAKDOWN POINTS; GAUSSIANS; INFLUENCE FUNCTIONS; LOAD FORECASTING; NEW APPROACHES; ONLINE IMPLEMENTATION; ROBUST ESTIMATION; ROBUST ESTIMATION METHOD; ROBUST METHODS;

ASYMPTOTIC ANALYSIS; PARAMETER ESTIMATION; REGRESSION ANALYSIS; TIME SERIES;

ELECTRIC LOAD FORECASTING;

EID: 77953801286     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2046413     Document Type: Article

References (23)

1. A. D. R. McQuarrie and C.-L. Tsai, Regression and Time Series Model Selection. River Edge, NJ: World Scientific, 1998.
2. P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, ser. Springer Series in Statistics, 2nd ed. New York: Springer-Verlag, 1991.
3. R. A. Maronna, R. D. Martin, and V. J. Yohai, "Theory and methods," in Robust Statistics, ser. Wiley Series in Probability and Statistics. Chichester, U.K.: Wiley, 2006.
4. O. H. Bustos and V. J. Yohai, "Robust estimates for ARMA models," J. Amer. Stat. Assoc., vol.81, no.393, pp. 155-168, 1986.
5. R. D. Martin and V. J. Yohai, "Influence functionals for time series," Ann. Stat., vol.14, no.3, pp. 781-855, 1986.
6. L. Mili, P. Panciatici, and Y. Chakhchoukh, "Robust short-term load forecasting using projection statistics," presented at the RTE-VTWorkshop, Paris, France, May 2006.
7. Y. Chakhchoukh, P. Panciatici, P. Bondon, and L. Mili, "A new robust estimation method for ARMA models," presented at the Int. Conf. Acoust., Speech, Signal Processing (ICASSP), Taipei, Taiwan, R.O.C., 2009.
8. M. Abramowitz and I. A. E. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Reprint of the 1972 ed. New York: Dover, 1992.
9. R. H. Jones, "Maximum likelihood fitting of ARMA models to time series with missing observations," Technometrics, vol.22, no.3, pp. 389-395, 1980.
10. C. J. Masreliez and R. D. Martin, "Robust Bayesian estimation for the linear model and robustifying the Kalman filter," IEEE Trans. Autom. Control, vol.AC-22, no.3, pp. 361-371, 1977.
11. L. Denby and R. D. Martin, "Robust estimation of the first order autoregressive parameter," J. Amer. Stat. Assoc., vol.74, no.365, pp. 140-146, 1979.
12. I. Silva and M. E. Silva, "Asymptotic distribution of the Yule-Walker estimator for INAR(p) processes," Stat. Probab. Lett., vol.76, no.15, pp. 1655-1663, 2006.
13. J. W. Taylor and P. E. McSharry, "Short-term load forecasting methods: An evaluation based on European data," IEEE Trans. Power Syst., vol.22, pp. 2213-2219, 2007.
14. R. Weron, Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach, ser. The Wiley Finance Series. New York: Wiley, 2006.
15. Réseau de Transport dElectricité (RTE) Power Consumption Archives RTE [Online]. Available: http://www.rte-france.com
16. K. C. Chanda, "Strong mixing properties of linear stochastic processes," J. Appl. Probab., vol.11, pp. 401-408, 1974.
17. R. Yokoyama, "On the Bahadur representation of sample quantiles for mixing processes," Tsukuba J. Math., vol.2, pp. 75-90, 1978.
18. K. B. Athreya and S. G. Pantula, "Mixing properties of Harris chains and autoregressive processes," J. Appl. Probab., vol.23, no.4, pp. 880-892, 1986.
19. R. J. Serfling, Approximation Theorems of Mathematical Statistics, ser. Wiley Series in Probability and Mathematical Statistics. New York: Wiley, 1980.
20. L. Soares and M. C. Medeiros, "Modeling and forecasting short-term electricity load: A comparison of methods with an application to Brazilian data," Int. J. Forecast., vol.24, no.4, pp. 630-644, 2008.
21. F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel, "The approach based on influence functions," in Robust Statistics, ser. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. New York: Wiley, 1986.
22. P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection, ser. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. New York: Wiley, 1987.
23. P. J. Huber, Robust Statistics, ser. Wiley Series in Probability and Mathematical Statistics. New York: Wiley, 1981.