Empirical likelihood for partial parameters in ARMA models with infinite variance. (English) Zbl 1442.62201

Summary: This paper proposes a profile empirical likelihood for the partial parameters in ARMA\((p, q)\) models with infinite variance. We introduce a smoothed empirical log-likelihood ratio statistic. Also, the paper proves a nonparametric version of Wilks’s theorem. Furthermore, we conduct a simulation to illustrate the performance of the proposed method.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G05 Nonparametric estimation
62G15 Nonparametric tolerance and confidence regions
Full Text: DOI


[1] Mikosch, T.; Gadrich, T.; Kluppelberg, C.; Adler, R. J., Parameter estimation for ARMA models with infinite variance innovations, The Annals of Statistics, 23, 1, 305-326 (1995) · Zbl 0822.62076
[2] Davis, R. A., Gauss-Newton and M-estimation for ARMA processes with infinite variance, Stochastic Processes and their Applications, 63, 1, 75-95 (1996) · Zbl 0902.62102
[3] Pan, J.; Wang, H.; Yao, Q., Weighted least absolute deviations estimation for ARMA models with infinite variance, Econometric Theory, 23, 5, 852-879 (2007) · Zbl 1237.62122
[4] Zhu, K.; Ling, S., The global LAD estimators for finite/infinite variance ARMA(p,q) models, Econometric Theory, 28, 5, 1065-1086 (2012) · Zbl 1251.91048
[5] Owen, A. B., Empirical likelihood ratio confidence intervals for a single functional, Biometrika, 75, 2, 237-249 (1988) · Zbl 0641.62032
[6] Owen, A. B., Empirical likelihood ratio confidence regions, The Annals of Statistics, 18, 1, 90-120 (1990) · Zbl 0712.62040
[7] Owen, A. B., Empirical Likelihood (2001), London, UK: Chapman and Hall, London, UK
[8] Monti, A. C., Empirical likelihood confidence regions in time series models, Biometrika, 84, 2, 395-405 (1997) · Zbl 0882.62082
[9] Chuang, C.; Chan, N. H., Empirical likelihood for autoregressive models, with applications to unstable time series, Statistica Sinica, 12, 2, 387-407 (2002)
[10] Chan, N. H.; Peng, L.; Qi, Y., Quantile inference for near-integrated autoregressive time series with infinite variance, Statistica Sinica, 16, 1, 15-28 (2006)
[11] Li, J.; Liang, W.; He, S.; Wu, X., Empirical likelihood for the smoothed LAD estimator in infinite variance autoregressive models, Statistics & Probability Letters, 80, 17-18, 1420-1430 (2010) · Zbl 1193.62049
[12] Li, J.; Liang, W.; He, S., Empirical likelihood for LAD estimators in infinite variance ARMA models, Statistics & Probability Letters, 81, 2, 212-219 (2011) · Zbl 1205.62133
[13] Brockwell, P. J.; Davis, R. A., Time series: Theory and Methods (1991), New York, NY, USA: Springer-Verlag, New York, NY, USA
[14] Phillips, P. C. B., A shortcut to LAD estimator asymptotics, Econometric Theory, 7, 4, 450-463 (1991)
[15] Silverman, B. W., Density Estimation for Statistics and Data Analysis (1986), London, UK: Chapman &Hall, London, UK
[16] de la Peña, V. H., A general class of exponential inequalities for martingales and ratios, The Annals of Probability, 27, 1, 537-564 (1999) · Zbl 0942.60004
[17] Qin, J.; Lawless, J., Empirical likelihood and general estimating equations, The Annals of Statistics, 22, 1, 300-325 (1994) · Zbl 0799.62049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.