On the Efficiency of Outlier Generating Mechanisms in Multivariate Time Series
Keywords:
Additive outlier, Convolution outlier, Innovative outlier, Multiplicative outlier, Vector auto regressive.Abstract
In this paper, two new outlier generating mechanisms for the detection of outliers in multivariate time series setting were derived. This is achieved by specifying two-variable vector autoregressive models and assuming additive and convolution effect of outliers on time series data. The magnitude and variance of outlier were derived for the generating models by method of least squares. Also a modified test statistics were developed to detect single outliers both in the response and explanatory variables. In order to establish the validity and efficiency of the derived models, the models were applied to both simulated and existing data. The results from the analysed data were also compared to some existing models and the result showed that the convolution model is best in terms of the number of outliers detected and the residual variance. This result confirms the finding in previous studies of outlier detection in univariate time series.
References
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[2] R. Baragona and F. Battaglia. “Outlier Detection in Multivariate Time Series by Independent Component Analysis.” Neutral Computation, 19:1962-1984.
[3] R. Baragona, F. Battaglia and C. Alzini. “Genetic Algorithms for the Identification of Additive and Innovational Outliers in Time Series” Computational Statistics and Data Analysis. 30,147,2001.
[4] V. Barnett. “The study of outliers: Purpose and Model.” Applied Statistics, 27(3), 242–250,1978.
[5] V. Barnett and T. Lewis. Outlier in Statistical Data. John Wiley & Sons U. K. 1994.
[6] G.E.P. Box, G.M. Jenkins and G. Reinsel. Time Series Analysis: Forecasting and Control,3rd Ed., New Jersey: Prentice-Hall,1994.
[7] K. Chaloner and R. Brant. “A Bayesian Approach to Outlier Detection and Residual Analysis.” Biometrika, 25, 651 – 660,1988.
[8] I. Chang, et. al. “Estimation of Time Series Parameters in the Presence of Outliers” Technometrics, 3, 193.204,1988.
[9] C. Chen and L.M. Liu. “Joint Estimation of Model Parameters and Outlier effects in Time Series.” Journal of the American Statistical Association, 88, 284 – 297,1993.
[10] D. Cucina, A.Di Salvatore and M. Protopapas. ‘’Meta-heuristic Methods for Outliers Detection in Multivariate Time Series.’’ Comisef working paper series, 003,270,2008
[11] A.J. Fox. “Outliers in Time Series.” Journal of the Royal Statistical Society. B34: 350 – 363,1972
[12] P. Galeano, D. Pena and R.S. Tsay. “Outlier Detection in Multivariate Time Series via Projection Pursuit.” Working paper 0-42. Statistics and Econometrics Series II, Dept. De Estadistica, Universidad Carlos III de Madrid,2004
[13] J. Helbling and R. Cleroux. “On Outlier Detection in Multivariate Time Series.” Mathematical Volume 34, Number 1, pp. 19-26,2009.
[14] A. Kaya. “Modelling Outlier Factors in Data Analysis.” Advances in Information Systems, LNCS 3261, 88 – 95,2010.
[15] A. Khattree and D.N. Naik. “Detection of Outliers in Bivariate Time Series Data.” Communications in Statistics – Theory and Methods, 16(12): 3701 – 3714,1987.
[16] G.M. Ljung. “On Outlier Detection in Time Series.” J. R. Statist. Soc. B. 55 No. 2, 559 -567,1993.
[17] C.R. Nelson, and C.L. Plosser. “Trends and Random Walks in Macroeconomic Time Series.” Journal of Monetary Economics, 10, 139 – 162,1982.
[18] D. Olivier and C. Amelie. “The Impact of Outliers on Transitory and Permanent Components in macroeconomic Series.” Economic Bulleting, Vol. 3, No 60 PP 1 – 9,2008.
[19] O. Olufolabo, O.I. Shittu and K.A. Adepoju. “Performance of Two Generating Mechanisms in Detection of Outliers in Multivariate Time Series.” American Journal of Theoretical and Applied Statistics.5(3), 115-122,2016.
[20] A. Pankratz. Forecasting with Univariate Box-Jenkins Models: Concepts and Cases, New York: John Wiley and Sins,1983.
[21] A. Pankratz. “Detecting and Treating Outliers in Dynamic Regression Models.” Biometrika,80, 47-54,1993.
[22] D. Pena and G.E.P. Box. “Identifying a Simplifying Structure in Time Series.” Journal of the American Statistical Association, 82, 836-843,1987.
[23] S. Ruey and R.S. Tsay. “Outliers, Level Shifts, and Variance Changes in Time Series.” Journal of Forecasting, Vol. 7, I-20 Department of Statistics, Carnegie Mellon University, U. S.A,1988.
[24] D.K. Shangodoyin. “On the Specification of time series Models in the Presence of Aberrant Observations”. Ph.D. Thesis in the Dept. of Statistics, Univ. of Ibadan,1994.
[25] I.O. Shittu and D.K. Shangodoyin. ‘’Detection of Outliers in Time Series Data: A Frequency Domain Approach.’’ Asian Journal of Scientific Research 1, (2) 130-137,2008.
[26] I. O. Shittu. “On Performance of Some Generating Models in Detection of Outliers Under Classical Rule.’’ M.Phil. Thesis. Dept. of Statistics, Univ. of Ibadan,2000.
[27] C. Sims. “Macroeconomics and Reality.” Econometricsa 48 (1), 11-46, JSTOR 112017,1980.
[28] R.S. Tsay. “Time Series Model specification in the Presence of Outlier.” Jour. Amer. Stat. Asso. 81, 132 – 141,1986.
[29] R.S. Tsay. “Outliers, Level Shifts and Variance Changes in Time Series.” Journal of Forecasting, 7, 1-20,1988.
[30] R.S. Tsay, D. Pena and A.E. Pankratz. “Outliers in multivariate time series.” Biometrika, 87, 789-804,2000.
[31] X.Wang. “Two-Phase Outlier Detection in Multivariate Time series.” Fuzzy Systems and Knowledge Discovery, Eighth International Conference. Vol.3,2011.
[32] Ji. Yanjie et al. (2013). “Detection of Outliers in a Time Series of Available Parking Spaces.” Mathematical Problems in Engineering, Volume 2013: 1-12,2013.
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Published
2016-07-19
How to Cite
Olufolabo, O. O., Shittu, O. I., & Adepoju, K. A. (2016). On the Efficiency of Outlier Generating Mechanisms in Multivariate Time Series. American Scientific Research Journal for Engineering, Technology, and Sciences, 22(1), 10–25. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/1771
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