A DOUBLY ROBUSTIFIED ESTIMATING FUNCTION FOR ARCH TIME SERIES MODELS

  • Kim, Sahm (Department of Statistics, Chung-Ang University) ;
  • Hwang, S.Y. (Department of Statistics, Sookmyung Women's University)
  • Published : 2007.09.30

Abstract

We propose a doubly robustified estimating function for the estimation of parameters in the context of ARCH models. We investigate asymptotic properties of estimators obtained as solutions of robust estimating equations. A simulation study shows that robust estimator from specified doubly robustified estimating equation provides better performance than conventional robust estimators especially under heavy-tailed distributions of innovation errors.

Keywords

References

  1. BASAWA, I. V., HUGGINS, R. M. AND STAUDTE, R. G. (1985). 'Robust tests for time series with an application to first-order autoregressive processes', Biometrika, 72, 559-571 https://doi.org/10.1093/biomet/72.3.559
  2. CHAN, W.-S. AND CHEUNG, S.-H. (1994). 'On robust estimation of threshold autoregressions', Journal of Forecasting, 13, 37-49 https://doi.org/10.1002/for.3980130106
  3. DENBY, L. AND MARTIN, R. D. (1979). 'Robust estimation of the first-order autoregressive parameter', Journal of the American Statistical Association, 74,140-146 https://doi.org/10.2307/2286743
  4. ENGLE, R. F. (1982). 'Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation', Econometrica, 50, 987-1007 https://doi.org/10.2307/1912773
  5. GODAMBE, V. P. (1985). 'The foundations of finite sample estimation in stochastic processes', Biometrika, 72, 419-428 https://doi.org/10.1093/biomet/72.2.419
  6. HUBER, P. J. (1981). Robust Statistics, John Wiley & Sons, New York
  7. HUI, Y. V. AND JIANG, J. (2005). 'Robust modelling of DTARCH models', The Econometrics Journal, 8,143-158 https://doi.org/10.1111/j.1368-423X.2005.00157.x
  8. KULKARNI, P. M. AND HEYDE, C. C. (1987). 'Optimal robust estimation for discrete time stochastic processes', Stochastic Processes and their Applications, 26, 267-276 https://doi.org/10.1016/0304-4149(87)90180-3
  9. LI, C. W. AND LI, W. K. (1996). 'On a double-threshold autoregressive heteroscedastic time series model', Journal of Applied Econometrics, 11, 253-274 https://doi.org/10.1002/(SICI)1099-1255(199605)11:3<253::AID-JAE393>3.0.CO;2-8
  10. MULER, N. AND YOHAI, V. J. (2002). 'Robust estimates for ARCH processes', Journal of Time Series Analysis, 23, 341-375 https://doi.org/10.1111/1467-9892.00268