Performance of Two Generating Mechanisms in Detection of Outliers in Multivariate Time Series
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 3, May 2016, Pages: 115-122
Received: Apr. 5, 2016; Accepted: Apr. 25, 2016; Published: May 10, 2016
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Olufolabo Olusesan Oluyomi., Department of Statistics, Yaba College of Technology, Yaba, Nigeria
Shittu Olarenwaju Ismail., Department of Statistics, University of Ibadan, Ibadan, Nigeria
Adepoju Kazeem Adesola., Department of Statistics, University of Ibadan, Ibadan, Nigeria
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This work is focused on developing two outlier generating mechanisms for the detection of outliers in the multivariate time series setting that is capable of ameliorating the swamping effect on regular observations in time series data. Specifying two-variable Vector Autoregressive (VAR) models and assuming innovative and multiplicative effect of outliers on time series data, the magnitude and variance of outlier were derived for the generating models by method of least squares. A modified test statistics were also developed to detect single outliers both in the response and explanatory variables. Real and simulated data were used to establish the validity of the models. The results show that the multiplicative is better than the additive model in terms of the number of outliers detected and the residual variance. This result is in line with previous studies in outlier detection in univariate time series.
Innovative Outlier, Additive Outlier, Multiplicative Outlier, Vector Auto Regressive
To cite this article
Olufolabo Olusesan Oluyomi., Shittu Olarenwaju Ismail., Adepoju Kazeem Adesola., Performance of Two Generating Mechanisms in Detection of Outliers in Multivariate Time Series, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 3, 2016, pp. 115-122. doi: 10.11648/j.ajtas.20160503.16
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A. Arribas-Gil, and J. Romo, “Shape Outlier Detection and Visualization for Functional Data: the Outliergram,” Biostatistics, 15, 603-619, 2014.
Z. Azami, A. Ibrahim, and S Mohd, S, “Detection Procedure for a Single Additive Outlier in Bilinear Model” Journal of Pak. Stat. Oper. Res. 1, 1-5, 2007.
R. Baragona, and F. Battaglia, “Outlier Detection in Multivariate Time Series by Independent Component Analysis”. Neutral Computation, 19: 1962-1984, 2007.
R. Baragona, F. Battaglia and D. Cucina, “Empirical Likelihood for Outlier Detection and Estimation in Autoregressive Time Series” Journal of Time Series Analysis Vol 37, 3, 315–336, 2015.
R. Baragona, F. Battaglia, and T. Calzini, “Genetic Algorithms for the Identification of Additive and Innovational Outliers in Time Series.’’ Computational Statistics and Data Analysis 30, 147, 2001.
V. Barnett, and T. Lewis, Outlier in Statistical Data, John Wiley & Sons U. K, 1995.
G. E. P. Box, G. M. Jenkins, and G. Reinsel, Time Series Analysis: Forecasting and Control, 3rd Ed., New Jersey:' Prentice-Hall, 1994.
K. Chaloner and R. Brant, “A Bayesian Approach to Outlier Detection and Residual Analysis,” Biometrika, 25, 651–660, 1988.
I. Chang, “Outlier in time series”. Technical Report, Department of statistics, University of Wisconsin, 1982.
I. Chang, G. D. Tiao, and C. Chen, “Estimation of Time Series Parameters in the Presence of Outliers. Technometrics,” 3, 193. 204, 1988.
S. Chattfield, The Analysis of Time series an introduction, New York, Charian and Hall, 1980.
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.
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.
L. Denby, and R. D. Martin, "Robust Estimation of the First Order Autoregressive Parameter," Journal of the American Statistical Association, 74, 140-146. 1979.
W. Enders, Applied Econometric Time Series, 2nd Edition, John Wiley & Sons, ISBN 0-471-23065-0, 2003.
M. Forni, and I. Reichlin, “Let's Get Real: A Dynamic Factor Analytical Approach to Disaggregated Business Cycle”. Review of Economic Studies, 65, 453/474, 1998.
A. J. Fox, “Outliers in Time Series”. Journal of the Royal Statistical Society. B34: 350 – 363, 1972.
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.
I. Georgiev, “A Factor Model for Innovational Outliers in Multivariate Time Series”, ICEE, First Italian Congress of Econometrics and Empirical Economics, Venice, 24-25, 2005.
A. Justel, D. Pena, and R. S. Tsay, “Detection of Outlier Patches in Autoregressive Time Series,” Statistica Sinica, 11, 651–673. 2000.
A. Kaya, “An Investigation: The Analysis of Outliers in Time Series”. PhD Thesis. Dokuz Fylit Unversity, Izmir, Turkey, 1999.
A. Kaya, “Modelling Outlier Factors in Data Analysis”, (advances in Information Systems), LNCS 3261, 88–95, 2010.
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.
N. D. Le, A. E. Raftery, and R. D. Martin, R. D. “Robust Order Selection in Autoregressive Models Using Robust Bayes Factors”. Journal of the American Statistical Association, 91, 123-131. 1996a.
G. M. Ljung, “On Outlier Detection in Time Series,” J. R. Statist. Soc. B. 55 No. 2, 559-567, 1993.
A. Luceno. Detecting Possibly Non-Consecutive Outliers in Industrial Time Series.
Journal of the Royal Statistical Society. Series B (Statistical Methodology), 60 (2): 295–310, 1998.
H. Lutkepohl, New Introduction to Multiple Time Series Analysis, Springer, Berlin, 2005.
R. E McCulloch, and R. S. Tsay, “Bayesian Analysis of Autoregressive Time Series Via the Gibbs sampler”, Journal of Time Series Analysis 15, 235–50, 1994.
C. R. Nelson, and C. I. Plosser, “Trends and Random Walks in Macroeconomic Time Series,” Journal of Monetary Economics, 10, 139–162, 1982.
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.
A. Pankratz, “Detecting and Treating Outliers in Dynamic Regression Models,” Biometrika, 80, 84'7-54, 1993.
D. Pena, and G. E. D. Box, “Identifying a Simplifying Structure in Time Series”, Journal of the American Statistical Association, 82, 836-843, 1987.
D. Pena, and A. Maravall, “Interpolations, Outliers and Inverse Autocorre¬lations", Communications in Statistics, Theory and Methods 20, 3175-86. 1991.
B. Rolin, “Comparing Classical and Resistant Outlier Rules,” Journal of American Stat. Ass. Vol. 412 pp. 1083–1090, 1990.
B. Rosner, “On the Detection of Many Outliers,” Technometrics. 17, 221–227, 1995.
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.
M. J. Sanchez, D and Pena, D. “The Identification of Multiple Outliers in ARIMA Models,” Communications in Statistics, Part A—Theory and Methods, 32, 1265–1287. 2003.
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.
I. O. Shittu, and D. K. Shangodoyin, “Detection of Outliers in Time Series Data: A Frequency Domain Approach’’ Assian Journal of Scientific Research 1, (2) 130-137, 2008.
I. O. Shittu, “On Performance of Some Generating Models in Detection of Outliers Under Classical Rule’’ Mphil Thesis Dept. of Statistics, Univ. of Ibadan, 2000.
C. Sims, “Macroeconomics and reality” Econometricsa 48 (1), JSTOR 112017, 1980.
S. Sridevi, S. Abirami, and S. Rajaram, “Detecting and Revamping of X-Outliers in Time Series Database,” International Journal of Computer Applications 60 (19): 28-33, 2012.
C. Robert and J. Helbling, “On Outlier Detection in Multivariate Time Series” Acta Mathematica Vietnamica, 34, 1, 19-26, 2009.
R. S. Tsay, “Time Series Model Specification in the Presence of Outlier”. Jour. Amer. Stat. Asso. 81, 132–141, 1986.
R. S. Tsay, “Outliers, Level Shifts and Variance changes in Time Series,” Journal of Forecasting, 7, 1-20, 1988.
R. S. Tsay, D. Pena, and A. E. Pankratz, “Outliers in Multivariate Time Series. Biometrika, 87, 789-804, 2000
Ji. Yanjie, D. Tang, A. Gou, P. T. Blythe and G. Reu, “Detection of Outliers in a Time Series of Available Parking Spaces,” Mathematical Problems in Engineering. Volume 2013: 1-12, 2013.
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