Abstract
The purpose of this contribution is to review outliers in both univariate and multivariate time series. The usual outlier types are presented in several frameworks including linear and nonlinear time series models. The key issues regarding identification of outliers and estimation of their effects in different settings are summarized.
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References
Baragona, R. (1998). Nonstationary time series, linear interpolators and outliers. Statistica, 58, 375–394.
Baragona, R., & Battaglia, F. (2007a). Outliers in dynamic factor models. Electronic Journal of Statistics, 1, 392–432.
Baragona, R., & Battaglia, F. (2007b). Outliers detection in multivariate time series by independent component analysis. Neural Computation, 19, 1962–1984.
Battaglia, F., & Orfei, L. (2005). Outlier detection and estimation in nonlinear time series. Journal of Time Series Analysis, 26, 107–121.
Battaglia, F., & Baragona, R. (1992). Linear interpolators and the outliers problem in time series. Metron, 50, 79–97.
Box, G. E. P., & Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems. Journal of the American Statistical Association, 70, 70–79.
Carnero, M. A., Peña, D., & Ruiz, E. (2007). Effects of outliers on the identification and estimation of GARCH models. Journal of Time Series Analysis, 28, 471–497.
Chang, I., Tiao, G. C., & Chen, C. (1988). Estimation of time series parameters in the presence of outliers. Technometrics, 30, 193–204.
Chen, C. W. S. (1997). Detection of additive outliers in bilinear time series. Computational Statistics & Data Analysis, 24, 283–294.
Chen, C., & Liu, L. M. (1993a). Joint estimation of model parameters and outlier effects in time series. Journal of the American Statistical Association, 88, 284–297.
Chen, C., & Liu, L. M. (1993b). Forecasting time series with outliers. Journal of Forecasting, 12, 13–35.
Davies, P. L., Fried, R., & Gather, U. (2004). Robust signal extraction for on-line monitoring data. Journal of Statistical Planning and Inference, 122, 65–78.
Doornik, J. A., & Ooms, M. (2005). Outlier detection in GARCH models. 2005-W24 Nuffield economics working papers.
Fokianos, C., & Fried, R. (2010). Interventions in INGARCH processes. Journal of Time Series Analysis, 31, 210–225.
Fox, A. J. (1972). Outliers in time series. Journal of the Royal Statistical Society. Series B. Methodological, 34, 350–363.
Franses, P. H., & Ghijsels, H. (1999). Additive outliers, GARCH and forecasting volatility. International Journal of Forecasting, 15, 1–9.
Gagné, C., & Duchesne, P. (2008). On robust forecasting in dynamic vector time series models. Journal of Statistical Planning and Inference, 138, 3927–3938.
Galeano, P., & Peña, D. (2012). Additive outlier detection in seasonal ARIMA models by a modified Bayesian information criterion. In W. R. Bell, S. H. Holan, & T. S. McElroy (Eds.), Economic time series: modeling and seasonality (pp. 317–336). Boca Raton: Chapman & Hall.
Galeano, P., Peña, D., & Tsay, R. S. (2006). Outlier detection in multivariate time series by projection pursuit. Journal of the American Statistical Association, 101, 654–669.
Gather, U., Bauer, M., & Fried, R. (2002). The identification of multiple outliers in online monitoring data. Estatistica, 54, 289–338.
Gelper, S., Schettlinger, K., Croux, C., & Gather, U. (2009). Robust online scale estimation in time series: a model-free approach. Journal of Statistical Planning and Inference, 139, 335–349.
Grané, A., & Veiga, H. (2010). Wavelet-based detection of outliers in financial time series. Computational Statistics & Data Analysis, 54, 2580–2593.
Haldrup, N., Montañes, A., & Sansó, A. (2011). Detection of additive outliers in seasonal time series. Journal of Time Series Econometrics, 3, 2.
Hotta, L. K., & Tsay, R. S. (2012). Outliers in GARCH processes. In W. R. Bell, S. H. Holan, & T. S. McElroy (Eds.), Economic time series: modeling and seasonality (pp. 337–358). Boca Raton: Chapman & Hall.
Justel, A., Peña, D., & Tsay, R. S. (2001). Detection of outlier patches in autoregressive time series. Statistica Sinica, 11, 651–673.
Kirkendall, N. J. (1992). Monitoring for outliers and level shifts in Kalman filter implementations of exponential smoothing. Journal of Forecasting, 11, 543–560.
Koehler, A. B., Snyder, R. D., Ord, J. K., & Beaumont, A. (2012). A study of outliers in the exponential smoothing approach to forecasting. International Journal of Forecasting, 28, 477–484.
Ljung, G. M. (1993). On outlier detection in time series. Journal of the Royal Statistical Society. Series B. Methodological, 55, 559–567.
Luceño, A. (1998). Detecting possibly non-consecutive outliers in industrial time series. Journal of the Royal Statistical Society. Series B. Methodological, 60, 295–310.
Maronna, R., Martin, R. D., & Yohai, V. (2006). Robust statistics. Chichester: Wiley.
Muler, N., Peña, D., & Yohai, V. (2009). Robust estimation for ARMA models. The Annals of Statistics, 37, 816–840.
Muler, N., & Yohai, V. (2008). Robust estimates for GARCH models. Journal of Statistical Planning and Inference, 138, 2918–2940.
Pankratz, A. (1993). Detecting and treating outliers in dynamic regression models. Biometrika, 80, 847–854.
Penzer, J. (2007). State space models for time series with patches of unusual observations. Journal of Time Series Analysis, 28, 629–645.
Peña, D., & Maravall, A. (1991). Interpolation, outliers and inverse autocorrelations. Communications in Statistics. Theory and Methods, 20, 3175–3186.
Perron, P., & Rodríguez, G. (2003). Searching for additive outliers in nonstationary time series. Journal of Time Series Analysis, 24, 193–220.
Sánchez, M. J., & Peña, D. (2010). The identification of multiple outliers in ARIMA models. Communications in Statistics. Theory and Methods, 32, 1265–1287.
Tsay, R. S. (1986). Time series model specification in the presence of outliers. Journal of the American Statistical Association, 86, 132–141.
Tsay, R. S. (1988). Outliers, level shifts and variance changes in time series. Journal of Forecasting, 7, 1–20.
Tsay, R. S., Peña, D., & Pankratz, A. E. (2000). Outliers in multivariate time series. Biometrika, 87, 789–804.
Acknowledgements
We gratefully acknowledge financial support by MCI grants SEJ2007/64500 and MTM2008-03010.
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Galeano, P., Peña, D. (2013). Finding Outliers in Linear and Nonlinear Time Series. In: Becker, C., Fried, R., Kuhnt, S. (eds) Robustness and Complex Data Structures. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35494-6_15
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DOI: https://doi.org/10.1007/978-3-642-35494-6_15
Publisher Name: Springer, Berlin, Heidelberg
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