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2017 | OriginalPaper | Chapter

Detection of Outlier in Time Series Count Data

Authors : Vassiliki Karioti, Polychronis Economou

Published in: Advances in Time Series Analysis and Forecasting

Publisher: Springer International Publishing

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Abstract

Outlier detection for time series data is a fundamental issue in time series analysis. In this work we develop statistical methods in order to detect outliers in time series of counts. More specifically we are interesting on detection of an Innovation Outlier (IO). Models for time series count data were originally proposed by Zeger (Biometrika 75(4):621–629, 1988) [28] and have subsequently generalized into GARMA family. The Maximum Likelihood Estimators of the parameters are discussed and the procedure of detecting an outlier is described. Finally, the proposed method is applied to a real data set.

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Literature
2.
go back to reference Barnett, V., Lewis, T.: Outliers in Statistical Data, 3rd edn. Wiley, Chichester (1994) Barnett, V., Lewis, T.: Outliers in Statistical Data, 3rd edn. Wiley, Chichester (1994)
3.
go back to reference Basu, S., Meckesheimer, M.: Automatic outlier detection for time series: an application to sensor data. Knowl. Inf. Syst. 11(2), 137–154 (2007)CrossRef Basu, S., Meckesheimer, M.: Automatic outlier detection for time series: an application to sensor data. Knowl. Inf. Syst. 11(2), 137–154 (2007)CrossRef
4.
go back to reference Benjamin, M.A., Rigby, R.A., Stasinopoulos, D.M.: Generalized autoregressive moving average models. J. Am. Stat. Assoc. 98(461), 214–223 (2003)MathSciNetCrossRefMATH Benjamin, M.A., Rigby, R.A., Stasinopoulos, D.M.: Generalized autoregressive moving average models. J. Am. Stat. Assoc. 98(461), 214–223 (2003)MathSciNetCrossRefMATH
5.
go back to reference Benjamin, M.A., Rigby, R.A., Stasinopoulos, M.D.: Fitting Non-Gaussian Time Series Models, pp. 191–196. Physica-Verlag HD, Heidelberg (1998) Benjamin, M.A., Rigby, R.A., Stasinopoulos, M.D.: Fitting Non-Gaussian Time Series Models, pp. 191–196. Physica-Verlag HD, Heidelberg (1998)
6.
go back to reference Blundell, R., Griffithand, R., Van Reenen, J.: Dynamic count data models of technological innovation. Econ. J. 105(429), 333–344 (1995)CrossRef Blundell, R., Griffithand, R., Van Reenen, J.: Dynamic count data models of technological innovation. Econ. J. 105(429), 333–344 (1995)CrossRef
7.
go back to reference Cardinal, M., Roy, R., Lambert, J.: On the application of integer-valued time series models for the analysis of disease incidence. Stat. Med. 18(15), 2025–2039 (1999)CrossRef Cardinal, M., Roy, R., Lambert, J.: On the application of integer-valued time series models for the analysis of disease incidence. Stat. Med. 18(15), 2025–2039 (1999)CrossRef
8.
go back to reference Davis, R., Holan, S., Lund, R., Ravishanker, N.: Handbook of Discrete-Valued Time Series. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. Taylor & Francis (2015) Davis, R., Holan, S., Lund, R., Ravishanker, N.: Handbook of Discrete-Valued Time Series. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. Taylor & Francis (2015)
9.
go back to reference Dunsmuir, W., Scott, D.: The glarma package for observation-driven time series regression of counts. J. Stat. Softw. 067(i07) (2015) Dunsmuir, W., Scott, D.: The glarma package for observation-driven time series regression of counts. J. Stat. Softw. 067(i07) (2015)
10.
go back to reference Ferdousi, Z., Maeda, A.: Unsupervised outlier detection in time series data. In: 22nd International Conference on Data Engineering Workshops (ICDEW’06), pp. x121–x121 (2006) Ferdousi, Z., Maeda, A.: Unsupervised outlier detection in time series data. In: 22nd International Conference on Data Engineering Workshops (ICDEW’06), pp. x121–x121 (2006)
12.
go back to reference Freeland, R.K., McCabe, B.P.M.: Analysis of low count time series data by Poisson autoregression. J. Time Ser. Anal. 25(5), 701–722 (2004)MathSciNetCrossRefMATH Freeland, R.K., McCabe, B.P.M.: Analysis of low count time series data by Poisson autoregression. J. Time Ser. Anal. 25(5), 701–722 (2004)MathSciNetCrossRefMATH
13.
go back to reference Heinen, A., Rengifo, E.: Multivariate autoregressive modeling of time series count data using copulas. J. Empirical Finan. 14(4), 564–583 (2007)CrossRef Heinen, A., Rengifo, E.: Multivariate autoregressive modeling of time series count data using copulas. J. Empirical Finan. 14(4), 564–583 (2007)CrossRef
14.
go back to reference Hotta, L., Neves, M.: A brief review on tests for detection of time series outliers. Estadistica 44(142, 143), 103–148 (1992) Hotta, L., Neves, M.: A brief review on tests for detection of time series outliers. Estadistica 44(142, 143), 103–148 (1992)
15.
go back to reference Johansson, P.: Speed limitation and motorway casualties: a time series count data regression approach. Accid. Anal. Prev. 28(1), 73–87 (1996)CrossRef Johansson, P.: Speed limitation and motorway casualties: a time series count data regression approach. Accid. Anal. Prev. 28(1), 73–87 (1996)CrossRef
16.
18.
go back to reference Karioti, V., Caroni, C.: Properties of the GAR(1) model for time series of counts. J. Modern Appl. Stat. Methods 5(1), 140–151 (2006)CrossRef Karioti, V., Caroni, C.: Properties of the GAR(1) model for time series of counts. J. Modern Appl. Stat. Methods 5(1), 140–151 (2006)CrossRef
19.
go back to reference Kedem, B., Fokianos, K.: Regression Models for Time Series Analysis. Wiley Series in Probability and Statistics. Wiley, New York (2005)MATH Kedem, B., Fokianos, K.: Regression Models for Time Series Analysis. Wiley Series in Probability and Statistics. Wiley, New York (2005)MATH
20.
go back to reference Li, W.K.: Time series models based on generalized linear models: some further results. Biometrics 50(2), 506–511 (1994)CrossRefMATH Li, W.K.: Time series models based on generalized linear models: some further results. Biometrics 50(2), 506–511 (1994)CrossRefMATH
21.
go back to reference Ljung, G.: On outlier detection in time series. J. R. Stat. Soc. Ser. B (Methodological) 55(2), 559–567 (1993) Ljung, G.: On outlier detection in time series. J. R. Stat. Soc. Ser. B (Methodological) 55(2), 559–567 (1993)
22.
go back to reference McCullagh, P., Nelder, J.: Generalized Linear Models, Second Edition. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Taylor & Francis (1989) McCullagh, P., Nelder, J.: Generalized Linear Models, Second Edition. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. Taylor & Francis (1989)
23.
go back to reference Quddus, M.A.: Time series count data models: an empirical application to traffic accidents. Accid. Anal. Prev. 40(5), 1732–1741 (2008)CrossRef Quddus, M.A.: Time series count data models: an empirical application to traffic accidents. Accid. Anal. Prev. 40(5), 1732–1741 (2008)CrossRef
24.
go back to reference Schmidt, A.M., Pereira, J.B.M.: Modelling time series of counts in epidemiology. Int. Stat. Rev. 79(1), 48–69 (2011)CrossRef Schmidt, A.M., Pereira, J.B.M.: Modelling time series of counts in epidemiology. Int. Stat. Rev. 79(1), 48–69 (2011)CrossRef
25.
go back to reference Thyregod, P., Carstensen, J., Madsen, H., Arnbjerg-Nielsen, K.: Integer valued autoregressive models for tipping bucket rainfall measurements. Environmetrics 10(4), 395–411 (1999)CrossRef Thyregod, P., Carstensen, J., Madsen, H., Arnbjerg-Nielsen, K.: Integer valued autoregressive models for tipping bucket rainfall measurements. Environmetrics 10(4), 395–411 (1999)CrossRef
26.
go back to reference Vogelvang, B.: Econometrics: Theory and Applications with EViews. Financial Times. Pearson/Addison Wesley (2005) Vogelvang, B.: Econometrics: Theory and Applications with EViews. Financial Times. Pearson/Addison Wesley (2005)
27.
go back to reference Yu, X., Baron, M., Choudhary, P.K.: Change-point detection in binomial thinning processes, with applications in epidemiology. Sequential Anal. 32(3), 350–367 (2013)MathSciNetCrossRefMATH Yu, X., Baron, M., Choudhary, P.K.: Change-point detection in binomial thinning processes, with applications in epidemiology. Sequential Anal. 32(3), 350–367 (2013)MathSciNetCrossRefMATH
29.
go back to reference Zeger, S.L., Qaqish, B.: Markov regression models for time series: a quasi-likelihood approach. Biometrics 44(4), 1019–1031 (1988)MathSciNetCrossRefMATH Zeger, S.L., Qaqish, B.: Markov regression models for time series: a quasi-likelihood approach. Biometrics 44(4), 1019–1031 (1988)MathSciNetCrossRefMATH
Metadata
Title
Detection of Outlier in Time Series Count Data
Authors
Vassiliki Karioti
Polychronis Economou
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-55789-2_15