Abstract
In this paper, we consider a stationary autoregressive AR(p) time series \(y_t=\phi _0+\phi _1y_{t-1}+\cdots +\phi _{p}y_{t-p}+u_t\). A self-weighted M-estimator for the AR(p) model is proposed. The asymptotic normality of this estimator is established, which includes the asymptotic properties under the innovations with finite or infinite variance. The result generalizes and improves the known one in the literature.
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References
An HZ, Chen ZG (1982) On convergence of LAD estimates in autoregression with infinite variance. J Multivar Anal 12:335–345
Chen Z, Li RZ, Wu YH (2012) Weighted quantile regression for AR model with infinite variance errors. J Nonparametr Stat 24:715–731
Davis RA (1996) Gauss–Newton and M-estimation for ARMA processes with infinite variance. Stoch Process Appl 63:75–95
Davis RA, Resnick SI (1985) Limit theory for moving averages of random variables with regularly varying tail probabilities. Ann Probab 13:179–195
Davis RA, Resnick SI (1986) Limit theory for the sample covariance and correlation functions of moving averages. Ann Stat 14:533–558
Davis RA, Knight K, Liu J (1992) M-estimation for autoregressions with infinite variance. Stoch Process Appl 40:145–180
Gross S, Steiger WL (1979) Least absolute deviation estimates in autoregression with infinite variance. J Appl Probab 16:104–116
Hannan EJ, Kanter M (1977) Autoregressive processes with infinite variance. J Appl Probab 14:411–415
Jansen D, de Vries CG (1991) On the frequency of large stock returns: putting booms and busts into perspective. Rev Econ Stat 73:18–28
Kanter M, Steiger WL (1974) Regression and autoregression with infinite variance. Adv Appl Probab 6:768–783
Koedijk KG, Schafgans MMA, de Vries CG (1990) The tail index of exchange rate returns. J Int Econ 29:93–108
Ling S (2005) Self-weighted least absolute deviation estimation for infinite variance autoregressive models. J R Stat Soc Ser B 67:381–393
Ling S (2007) Self-weighted and local quasi-maximun likelihood estimator for ARMA-GARCH/IGARCH models. J Econom 140:849–873
Pan B, Chen M (2013) Self-weighted quasi-maximum exponential likelihood estimator for ARFIMA-GARCH model. J Stat Plan Inference 143:716–729
Pan J, Wang H, Yao Q (2007) Weighted least absolute deviations estimation for ARMA models with infinite variance. Econom Theory 23:852–879
Pan BG, Chen M, Wang Y, Xia W (2015) Weight least absolute deviations estimation for ARFIMA time series with finite or infinite variance. J Korean Stat Soc 44:1–11
Acknowledgments
The authors thank the Editor in Chief Prof. Norbert Henze and the anonymous referee for their helpful comments and valuable suggestions that greatly improved the paper. This work is supported by the National Natural Science Foundation of China (11526033, 11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1608085QA02, 1408085QA02), the Science Fund for Distinguished Young Scholars of Anhui Province (1508085J06) and Introduction Projects of Anhui University Academic and Technology Leaders.
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Wang, X., Hu, S. Asymptotics of self-weighted M-estimators for autoregressive models. Metrika 80, 83–92 (2017). https://doi.org/10.1007/s00184-016-0592-x
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DOI: https://doi.org/10.1007/s00184-016-0592-x