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Identification and Modeling of Outliers in a Discrete - Time Stochastic Series

Received: 27 February 2017     Accepted: 8 April 2017     Published: 5 July 2017
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Abstract

This study was prompted by the fact that the presence of outliers in discrete-time stochastic series may result in model misspecification, biases in parameter estimation and in addition, it is difficult to identify some outliers due to masking effects. However, the iterative approach which involves joint estimation of outliers effects and model parameters appears to be a panacea for masking effects. Considering the dataset on credit to private sector in Nigeria from 1981 to 2014, we found that ARIMA (1, 1, 1) model fitted well to the series without considering the presence of outliers. Using the iterative procedure method to reduce masking effects, the following outliers, IO (t = 24), AO (t = 33) and TC (t = 22) were identified. Adjusting the series for outliers and iterating further, ARIMA (2, 0, 1) model alongside AO (t = 33) and TC (t = 22) outliers was found to fit the series better than ARIMA (1, 1, 1) model. The implication is that in the presence of outliers, ARIMA (1, 1, 1) model was misspecified, the order of integration was wrong and by extension, autocorrelation and partial autocorrelation functions were misleading, and the estimated parameters were biased.

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 4)
DOI 10.11648/j.ajtas.20170604.14
Page(s) 191-197
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

ARIMA Model, Discrete - Time Stochastic Series, Masking Effects, Outlier Effects, Outlier Types

References
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[3] Akpan, E. A. and Moffat, I. U. (2016). Dynamic Time Series Regression: A Panacea for Spurious Correlations. International Journal of Scientific and Research Publications 6(1): 337–342.
[4] Battaglia, F. and Orfei, L. (2002). Outlier Detection and Estimation in Nonlinear Time Series. Journal of Time Series Analysis, 26(1): 108–120.
[5] Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (2008). Time Series Analysis: Forecasting and Control. 3rd ed., New Jersey: Wiley and sons.
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[7] Chang, I., Tiao, G. C. and Chen, C. (1988). Estimation of Time Series Parameters in the Presence of Outliers. Technometrics, 30, 193–204.
[8] Chen, C. and Liu, L. M. (1993). Joint Estimation of Model Parameters and Outlier Effects in Time Series. Journal of the American Statistical Association, 8, 284–297.
[9] Ebong, D. W. (1998). Markov Chains and Applications. Footstep Publications, Port Harcourt. p 8.
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[11] Fuller, W. A. (1996). Introduction to Statistical Time Series, 2nd Ed., New York, John Wiley and Sons.
[12] Galeano, P. and Pena, D. (2013). Finding Outliers in Linear and Nonlinear Time Series. Available at halweb.uc3m.es/esp/personal/personas/dpena/publications/ingles/2013 GatherBook- galeano.pdf. Accessed 25 November, 2016.
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[18] Kaya, A. (2010). Statistical Modeling for Outliers Factors. Ozean Journal of Applied Science, 3(1): 185-194.
[19] Sanchez, M. J. and Pena, D. (2010). The Identification of Multiple Outliers in ARIMA Models.
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  • APA Style

    Imoh Udo Moffat, Emmanuel Alphonsus Akpan. (2017). Identification and Modeling of Outliers in a Discrete - Time Stochastic Series. American Journal of Theoretical and Applied Statistics, 6(4), 191-197. https://doi.org/10.11648/j.ajtas.20170604.14

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    ACS Style

    Imoh Udo Moffat; Emmanuel Alphonsus Akpan. Identification and Modeling of Outliers in a Discrete - Time Stochastic Series. Am. J. Theor. Appl. Stat. 2017, 6(4), 191-197. doi: 10.11648/j.ajtas.20170604.14

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    AMA Style

    Imoh Udo Moffat, Emmanuel Alphonsus Akpan. Identification and Modeling of Outliers in a Discrete - Time Stochastic Series. Am J Theor Appl Stat. 2017;6(4):191-197. doi: 10.11648/j.ajtas.20170604.14

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  • @article{10.11648/j.ajtas.20170604.14,
      author = {Imoh Udo Moffat and Emmanuel Alphonsus Akpan},
      title = {Identification and Modeling of Outliers in a Discrete - Time Stochastic Series},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {4},
      pages = {191-197},
      doi = {10.11648/j.ajtas.20170604.14},
      url = {https://doi.org/10.11648/j.ajtas.20170604.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170604.14},
      abstract = {This study was prompted by the fact that the presence of outliers in discrete-time stochastic series may result in model misspecification, biases in parameter estimation and in addition, it is difficult to identify some outliers due to masking effects. However, the iterative approach which involves joint estimation of outliers effects and model parameters appears to be a panacea for masking effects. Considering the dataset on credit to private sector in Nigeria from 1981 to 2014, we found that ARIMA (1, 1, 1) model fitted well to the series without considering the presence of outliers. Using the iterative procedure method to reduce masking effects, the following outliers, IO (t = 24), AO (t = 33) and TC (t = 22) were identified. Adjusting the series for outliers and iterating further, ARIMA (2, 0, 1) model alongside AO (t = 33) and TC (t = 22) outliers was found to fit the series better than ARIMA (1, 1, 1) model. The implication is that in the presence of outliers, ARIMA (1, 1, 1) model was misspecified, the order of integration was wrong and by extension, autocorrelation and partial autocorrelation functions were misleading, and the estimated parameters were biased.},
     year = {2017}
    }
    

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    AU  - Imoh Udo Moffat
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    Y1  - 2017/07/05
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    DO  - 10.11648/j.ajtas.20170604.14
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
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    AB  - This study was prompted by the fact that the presence of outliers in discrete-time stochastic series may result in model misspecification, biases in parameter estimation and in addition, it is difficult to identify some outliers due to masking effects. However, the iterative approach which involves joint estimation of outliers effects and model parameters appears to be a panacea for masking effects. Considering the dataset on credit to private sector in Nigeria from 1981 to 2014, we found that ARIMA (1, 1, 1) model fitted well to the series without considering the presence of outliers. Using the iterative procedure method to reduce masking effects, the following outliers, IO (t = 24), AO (t = 33) and TC (t = 22) were identified. Adjusting the series for outliers and iterating further, ARIMA (2, 0, 1) model alongside AO (t = 33) and TC (t = 22) outliers was found to fit the series better than ARIMA (1, 1, 1) model. The implication is that in the presence of outliers, ARIMA (1, 1, 1) model was misspecified, the order of integration was wrong and by extension, autocorrelation and partial autocorrelation functions were misleading, and the estimated parameters were biased.
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Author Information
  • Department of Mathematics and Statistics, University of Uyo, Uyo, Nigeria

  • Department of Mathematics and Statistics, University of Uyo, Uyo, Nigeria

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