Abstract
It is known that the occurrence of outliers in linear or non-linear time series models may have adverse effects on the modelling and statistical inference of the data. Consequently, extensive research has been conducted on developing outlier detection procedures so that outliers may be properly managed. However, no work has been done on the problem of outliers in circular time series data. This problem is the focus of this paper. The main objective is to develop novel numerical and graphical procedures for detecting these outliers in circular time series data.A number of circular time series models have been proposed including the circular autoregressive model. We extend the iterative outlier detection procedure which has been successfully used in linear time series models to the circular autoregressive model. The proposed procedure shows a good performance when investigated via simulation for the circular autoregressive model of order one. At the same time, several statistical techniques have been used to detect the change of preferred trend in time series data using SLIME and CUSUM plots. While the methods fail to indicate directly the outliers in circular time series data, we use the ideas employed to develop three novel graphical procedures for identifying the outliers. For illustration, we apply the procedures to a particular set of wind direction data. An agreement between the results of the graphical and iterative detection procedures is observed. These procedures could be very useful in improving the modelling and inferential processes for circular time series data.
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References
Abraham B, Chuang A (1989) Outlier detection and time series modelling. Technometric 31:241–248
Abuzaid AH, Mohamed IB, Hussin AG (2009) A new test of discordancy in circular data. Commun Stat-Simul Comput 38(4):682–691
Abuzaid AH, Mohamed IB, Hussin AG (2012) Boxplot for circular variables. Comput Stat 27(3):381–392
Artes R, Toloi CMC (2010) An autoregressive model for time series of circular data. Commun Stat-Theory Methods 39:186–194
Bagchi P, Guttman I (1990) Spuriosity and outliers in directional data. J Appl Stat 17:341–350
Bulla J, Lagona F, Marouotti A, Picone M (2012) A multivariate hidden Markov model for the identification of Sea regimes from incomplete skewed and circular time series. J Agric, Biol Environ Stat 17(4):544–567
Cameron MA (1983) The comparison of time series recorders. Technometrics 25:9–22
Charles A, Darné O (2005) Outliers and GARCH models in financial data. Econ Lett 86(3):347–352
Chen C, Liu L-M (1993) Joint estimation of model parameters outlier effects in time series. J Am Stat Assoc 88(421):284–297
Choy K (2001) Outlier detection for stationary time series. J Stat Plan Inference 99:111–127
Collett D (1980) Outliers in circular data. Appl Stat 29(1):50–57
Craig, PS (1988) Time series analysis for directional data. Ph.D thesis, Trinity College Dublin, Dublin
Fisher NI, Lee AJ (1992) Regression models for an angular response. Biometrics 48:665–677
Fisher NI, Lee AJ (1983) A correlation coefficient for circular data. Biometrika 70:327–332
Fisher NI (1993) Statistical Analysis of Circular Data. Cambridge University Press, Cambridge
Fisher NI, Lee AJ (1994) Time series analysis of circular data. J Roy Stat Soc Ser B 56(2):327–339
Fox AJ (1972) Outliers in time series. J Roy Stat Soc Ser B 34(3):350–363
Holzmann H, Munk A, Suster M, Zucchini W (2006) Hidden Markov models for circular and linear-circular time series. Environ Ecol Stat 13:325–347
Hussin AG, Fieller NRJ, Stillman EC (2004) Linear regression for circular variables with application to directional data. J Appl Sci Technol 9(1&2):1–6
Jammalamadaka SR, SenGupta A (2001) Topics in Circular Statistics. World Scientific Press, Singapore
Mardia KV (1975) Statistics of directional data. J R Stat Soc Ser B 37:349–393
Mohamed IB, Ismail MI, Yahya MS, Hussin AG, Mohamed N, Zaharim A, Zainol MS (2011) Improvement on the innovational outlier detection procedure in a bilinear model. Sains Malays 40(2):191–196
Peña D, Maravall A (1991) Interpolation, outliers and inverse autocorrelations. Commun Stat Theory Methods 20(10):3175–3186
Shepherd J, Fisher NI (1982) Rapid method of mapping fracture trends in collieries. Trans Soc Min Eng AIME 270:1931–1933
Tsay RS (1988) Outliers, level shifts, and variance changes in time series. J Forecast 7(1):1–20
Upton G (1993) Testing for outliers in circular data. J Appl Stat 20(2):229–235
Watson GS, Beran RJ (1967) Testing a sequence of unit vectors for serial correlation. J Geophys Res 72:5655–5659
Acknowledgments
The authors thank the Associate Editor and the reviewers for their valuable comments and suggestions. The research is partially supported by the Fundamental Research Grant Scheme, Malaysia (No. FP012-2013A).
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Handling Editor: Pierre Dutilleul.
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Abuzaid, A.H., Mohamed, I.B. & Hussin, A.G. Procedures for outlier detection in circular time series models. Environ Ecol Stat 21, 793–809 (2014). https://doi.org/10.1007/s10651-014-0281-8
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DOI: https://doi.org/10.1007/s10651-014-0281-8