Evaluation of Test Statistics for Detection of Outliers and Shifts

  • Amena Urooj Pakistan Institute of Development Economics, Islamabad, Pakistan. https://orcid.org/0000-0003-4626-5525
  • Zahid Asghar Quaid-e-Azam University, Islamabad, Pakistan.
Keywords: discordant observations, structural breaks, simulation analysis, additive outlier, innovative outlier, transient change, level shift, iterative procedure, R (Library (TSA))


Existence of outliers and structural breaks having mutually unknown nature, in time series data, offer challenges to data analysts in model identification, estimation and validation. Detection of these outliers has been an important area of research in time series since long. To analyze the impact of these structural breaks and outliers on model identification, estimation and their inferential analysis, we use two data generating processes: MA(1) and ARMA(1,1). The performance of the test statistics for detecting additive outlier(AO), innovative outlier(IO), level shift(LS) and transient change(TC) is investigated using simulation strategy through power of a test, empirical level of significance, empirical critical values, misspecification frequencies and sampling distribution of estimators for the two models. The empirical critical values are found higher than the theoretical cut-off points, empirical power of the test statistics is not satisfactory for small sample size, large cut-off points and large model coefficient. We have explored confusion between LS, AO, TC and IO at different critical values(c) by varying sample size. We have also collected empirical evidence from time series data for Pakistan using 3-stage iterative procedure to detect multiple outliers and structural breaks. We find that neglecting shocks lead to wrong identification, biased estimation and excess kurtosis.

JEL Classification Codes: C15, C18, C63, C32, C87, C51, C52, C82

AMS Classification Codes: 62, 65, 91, DI, 62-08, 62J20, 00A72, 91-08, 91-10, 91-11 62P20, 91B82, 91B84, 62M07, 62M09, 62M10, 62M15, 62M20


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Box, G. E., & Jenkins, G. M. (1976). Time series analysis: forecasting and control, revised ed. Holden-Day. Retrieved from https://www.amazon.com/Time-Analysis-Forecasting-Control-Hardcover/dp/B011SJ22JI.

Chang, I., Tiao, G. C., & Chen, C. (1988). Estimation of time series parameters in the presence of outliers. Technometrics, 30(2), 193-204. https://doi.org/10.1080/00401706.1988.10488367.

Chen, C., & Liu, L. M. (1993). Joint estimation of model parameters and outlier effects in time series. Journal of the American Statistical Association, 88(421), 284-297. https://doi.org/10.1080/01621459.1993.10594321.

Fox, A. J. (1972). Outliers in time series. Journal of the Royal Statistical Society: Series B (Methodological), 34(3), 350-363. https://doi.org/10.1111/j.2517-6161.1972.tb00912.x.

Kaiser, R., & Maravall, A. (2001). Seasonal Outliers in Time Series, Estadıstica. Journal of the Inter-American Statistical Institute, 53, 101-142.

Pena, D. (1990). Influential observations in time series. Journal of Business & Economic Statistics, 8(2), 235-241. https://doi.org/10.1080/07350015.1990.10509795.

Tsay, R. S. (1986). Time series model specification in the presence of outliers. Journal of the American Statistical Association, 81(393), 132-141. https://doi.org/10.1080/01621459.1986.10478250.

Tsay, R. S. (1988). Outliers, level shifts, and variance changes in time series. Journal of Forecasting, 7(1), 1-20. https://doi.org/10.1002/for.3980070102.

Urooj, A. (2016). Performance of Time Series Models under Structural Discontinuities and Discordant Observations. [Unpublished Ph.D. thesis]. Quaid-i-Azam University.

Urooj, A., & Asghar, A. (2017). Analysis of the performance of test statistics for detection of outliers (additive, innovative, transient, and level shift) in AR (1) processes, Communications in Statistics-Simulation and Computation, 46(2), 948-979. https://doi.org/10.1080/03610918.2014.985383.

How to Cite
Urooj, A., & Asghar, Z. (2020). Evaluation of Test Statistics for Detection of Outliers and Shifts. Journal of Quantitative Methods, 4(2), 54-75. https://doi.org/10.29145/2020/jqm/040203