Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T17:59:04.306Z Has data issue: false hasContentIssue false
  • English
  • Français

THE GLOBAL WEIGHTED LAD ESTIMATORS FOR FINITE/INFINITE VARIANCE ARMA(p,q) MODELS

Published online by Cambridge University Press:  27 April 2012

Ke Zhu  and
Shiqing Ling
Ke Zhu
Affiliation:
Hong Kong University of Science and Technology
Shiqing Ling*
Affiliation:
Hong Kong University of Science and Technology
*
*Address correspondence to Shiqing Ling, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates the global self-weighted least absolute deviation (SLAD) estimator for finite and infinite variance ARMA(p, q) models. The strong consistency and asymptotic normality of the global SLAD estimator are obtained. A simulation study is carried out to assess the performance of the global SLAD estimators. In this paper the asymptotic theory of the global LAD estimator for finite and infinite variance ARMA(p, q) models is established in the literature for the first time. The technique developed in this paper is not standard and can be used for other time series models.

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 5 , October 2012 , pp. 1065 - 1086
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bloomfield, P. & Steiger, W.L. (1983) Least absolute deviations. Theory, applications, and algorithms. In Progress in Probability and Statistics, vol. 6. Birkhäuser Boston.Google Scholar
Davis, R.A. (1996) Gauss-Newton and M-estimation for ARMA processes with infinite variance. Stochastic Processes and Their Applications 63, 75–95.Google Scholar
Davis, R.A. & Dunsmuir, W.T.M. (1997) Least absolute deviation estimation for regression with ARMA errors. Journal of Theoretical Probability 10, 481–497.Google Scholar
Davis, R.A., Knight, K., & Liu, J. (1992) M-estimation for autoregressions with infinite variance. Stochastic Processes and Their Applications 40, 145–180.Google Scholar
Davis, R.A. & Wu, W. (1997) Bootstrapping M-estimates in regression and autoregression with infinite variance. Statistica Sinica 7, 1135–1154.Google Scholar
Dunsmuir, W.T.M. & Spencer, N.M. (1991) Strong consistency and asymptotic normality of L 1 estimates of the autoregressive moving-average model. Journal of Time Series Analysis 12, 95–104.Google Scholar
Durrett, R. (2005) Probability: Theory and Examples. 3rd ed. Thomson-Brooks/Cole.Google Scholar
Huber, P.J. (1967) The behavior of maximum likelihood estimates under nonstandard conditions. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 221–233. University of California Press.Google Scholar
Knight, K. (1987) Rate of convergence of centred estimates of autoregressive parameters for infinite variance autoregressions. Journal of Time Series Analysis 8, 51–60.CrossRefGoogle Scholar
Knight, K. (1998) Limiting distributions for L 1 regression estimators under general conditions. Annals of Statistics 26, 755–770.Google Scholar
Koenker, R.W. & Bassett, G.W. (1978) Regression quantiles. Econometrica 46, 33–50.Google Scholar
Koenker, R.W. & Bassett, G.W. (1982) Robust tests for heteroscedasticity based on regression quantiles. Econometrica 50, 43–61.Google Scholar
Koenker, R. & Zhao, Q.S. (1996) Conditional quantile estimation and inference for ARCH models. Econometric Theory 12, 793–813.Google Scholar
Ling, S. (2005) Self-weighted least absolute deviation estimation for infinite variance autoregressive models. Journal of the Royal Statistical Society, Series B 67, 381–393.CrossRefGoogle Scholar
Ling, S. (2007) Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models. Journal of Econometrics 140, 849–873.Google Scholar
Ling, S. & McAleer, M. (2003) Asymptotic theory for a new vector ARMA-GARCH model. Econometric Theory 19, 280–310.Google Scholar
Mikosch, T., Gadrich, T., Klüppelberg, C., & Adler, R.J. (1995) Parameter estimation for ARMA models with infinite variance innovations. Annals of Statistics 23, 305–326.Google Scholar
Pan, J., Wang, H., & Yao, Q. (2007) Weighted least absolute deviations estimation for ARMA models with infinite variance. Econometric Theory 23, 852–879.Google Scholar
Pollard, D. (1985) New ways to prove central limit theorems. Econometric Theory 1, 295–314.Google Scholar
Pollard, D. (1991) Asymptotics for least absolute deviation regression estimators. Econometric Theory 7, 186–199.Google Scholar
Rachev, S.T. (2003) Handbook of Heavy Tailed Distributions in Finance. Elsevier/North-Holland.Google Scholar
Wu, R. & Davis, R.A. (2009) Least absolute deviation estimation for general autoregressive moving average time series models. Journal of Time Series Analysis 31, 98–112.Google Scholar
Zhu, K. & Ling, S. (2011) Global self-weighted and local quasi-maximum exponential likelihood estimations for ARMA-GARCH/IGARCH models. Annals of Statistics 39, 2131–2163.Google Scholar
Zhu, K. & Ling, S. (2012) Quasi-maximum exponential likelihood estimators for a double AR(p) model. Statistica Sinica, forthcoming.Google Scholar