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Robust estimation in time series

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Abstract

The main purpose of this work is to study empirically by means of simulations, the robustness of a set of proposals to estimate the parameters in the MA(1) time series model. The non-normal populations are mixtures of normal distributions, defined byg(x)=pN(0,k)+(1-p)N(0,1), where the proportion of contamination most frequently used isp=0.10 andk is the variance of the distribution used in the contamination; α is taken to be 0.90, which is close to the region of non-invertibility. Key results are that the estimation procedures used in the study provide good results in terms of biases in the estimation of the parameters, and that the biases are not changed when contaminated errors (mixtures) are considered. The estimation of the variance of the contaminated errors is also studied through simulations.

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References

  • Aitkin, M. andTunnicliffe, W. G. (1980). Mixtures models, outliers and the EM algorithm.Technometrics, 22:325–331.

    Article  MATH  Google Scholar 

  • Anderson, T. W. andMentz, R. P. (1980). On the structure of the likelihood function of autoregressive and moving average models.Journal of Time Series Analysis, 1:83–94.

    MATH  MathSciNet  Google Scholar 

  • Anderson, T. W. andMentz, R. P. (1993a). Evaluation of quadratic forms and traces for iterative estimation in first-order moving average models.Communications in Statistics: Theory and Methods, 22:931–963.

    MATH  MathSciNet  Google Scholar 

  • Anderson, T. W. andMentz, R. P. (1993b).Iterative Procedures for Exact Maximum Likelihood Estimation in the First-order Gaussian Moving Average Model. A Raghu Raj Bahadur Fetchrift. Wiley Eastern Limited.

  • Anderson, T. W., Mentz, R. P., Jarma, N. M., andMartínez, C. I. (1996). Simulations of iterative procedures for maximum likelihood estimation in MA(1) models.Communications in Statistics: Simulation and Computation, 25:851–865.

    MATH  MathSciNet  Google Scholar 

  • Anderson, T. W. andTekemura, A. (1986). Why do noninverrible estimated moving averages occur?Journal of Time Series Analysis, 7:235–254.

    MATH  MathSciNet  Google Scholar 

  • Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H., andTukey, J. W. (1972).Robust estimates of location: survey and advances. Princeton University Press, Princeton.

    MATH  Google Scholar 

  • BMDP (1990),BMDP Statistical Software. Los Angeles, California.

  • Box, G. E. P. andJenkins, G. M. (1970).Time Series Analysis Forecasting and Control. Holden-Day, San Francisco.

    MATH  Google Scholar 

  • Box, G. E. P. andTiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems.Journal of the American Statistical Association, 70:70–79.

    Article  MATH  MathSciNet  Google Scholar 

  • Brockwell, P. J. andDavis, R. A. (1991).ITSM: An Interactive Time Series Modelling Package for the PC. Springer-Verlag, New York.

    MATH  Google Scholar 

  • Chang, I., Tiao, G. C., andChan, C. (1988). Estimation of Time Series parameters in the presence of outliers.Technometrics, 30:193–204.

    Article  MathSciNet  Google Scholar 

  • Cook, R. D. andWeisberg, S. (1982).Residuals and influence in regression, Chapman and Hall, London.

    MATH  Google Scholar 

  • Fox, A. J. (1972). Outliers in Time Series,Journal of the Royal Statistical Society, B 43:350–363.

    Google Scholar 

  • Lindsay, B. G. (1995). Mixture models: theory, geometry and applications, Regional conference series in probability and statistics, Institute of Mathematical Statistics.

  • Martin, R. D. (1980). Robust estimation of autoregressive models. Directions in time series. Institute of Mathematical Statistics, Hayward, California.

    Google Scholar 

  • MINITAB (1996).Guía del Usuario de MINITAB en Español, Versión 2 para Windows. Minitab Inc., Los Angeles, California, US.

    Google Scholar 

  • Peña, D. (1990). Influential observations in Time Series,Journal of Business and Economics Statistics, 8:235–241.

    Article  Google Scholar 

  • Tikku, M. L., Wong, W. K., Vaughan, D. C., andBian, G. (2000). Time Series models in non-normal situations: symmetric innovations.Journal of Time Series Analysis, 21:571–596.

    Article  MathSciNet  Google Scholar 

  • Venables, W. N. andRipley, B. D. (1997).Modern Applied Statistics with S-Plus. Springer-Verlag, New York, 2nd ed.

    MATH  Google Scholar 

  • Wolfram, S. (1991).Mathematica, Addison-Wesley Publishing Co., Reading, Massachusetts US, 2nd ed.

    Google Scholar 

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Authors and Affiliations

  1. Faciltad de Ciencias Económicas, Universidad Nacional de Tucumán and CONICET (Argentina), Casilla de Correo 209, 4000, Tucumán, Argentina

    Raúl P. Mentz & Carlos I. Martínez

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  1. Raúl P. Mentz
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  2. Carlos I. Martínez
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Correspondence to Raúl P. Mentz.

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Mentz, R.P., Martínez, C.I. Robust estimation in time series. Test 11, 385–404 (2002). https://doi.org/10.1007/BF02595713

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  • DOI: https://doi.org/10.1007/BF02595713

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