Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-23T15:11:17.092Z Has data issue: false hasContentIssue false
  • English
  • Français

TOWARD A UNIFIED INTERVAL ESTIMATION OF AUTOREGRESSIONS

Published online by Cambridge University Press:  25 November 2011

Ngai Hang Chan ,
Deyuan Li  and
Liang Peng
Get access Rights & Permissions [Opens in a new window]

Abstract

An empirical likelihood–based confidence interval is proposed for interval estimations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its asymptotic limit is always normal without assuming stationarity of the process. Unlike the bootstrap method or the least squares procedure, the proposed empirical likelihood–based confidence interval is applicable regardless of whether the underlying autoregressive process is stationary, unit root, near-integrated, or even explosive, thereby providing a unified approach for interval estimation of an AR(1) model to encompass all situations. Finite-sample simulation studies confirm the effectiveness of the proposed method.

Type
Brief Report
Information
Econometric Theory , Volume 28 , Issue 3 , June 2012 , pp. 705 - 717
Copyright
Copyright © Cambridge University Press 2011

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.)

Footnotes

We thank three anonymous referees, the editor, and the co-editor Giuseppe Cavaliere for helpful references and constructive suggestions, which led to an improved version of this note. This research was supported in part by grants from HKSAR-RGC-GRF nos. 400306, 400308, and 400410, NSA grant no. H98230-10-1-0170, NSF grant no. DMS1005336, and NNSFC grant no. 10801038.

References

REFERENCES

Chan, N.H. (1990) Inference for near-integrated time series with infinite variance. Journal of the American Statistical Association 85, 1069–1074.Google Scholar
Chan, N.H. (2009) Time series with roots on or near the unit circle. In Andersen, T.G., Davis, R.A., Kreiss, J., & Mikosch, T. (eds.), Springer Handbook of Financial Time Series, pp. 695–707. Springer-Verlag.Google Scholar
Chan, N.H. & Peng, L. (2005) Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors. Biometrika 92, 477–484.Google Scholar
Chan, N.H., Peng, L., & Qi, Y. (2006) Quantile inference for near-integrated autoregressive time series with infinite variance. Statistica Sinica 16, 15–28.Google Scholar
Chan, N.H. & Wei, C.Z. (1987) Asymptotic inference for nearly nonstationary AR(1) processes. Annals of Statistics 15, 1050–1063.Google Scholar
Chan, N.H. & Zhang, R.M. (2009) Inference for nearly nonstationary processes under strong dependence and infinite variance. Statistica Sinica 19, 925–947.Google Scholar
Chuang, C. & Chan, N.H. (2002) Empirical likelihood for autoregressive models, with applications to unstable time series. Statistica Sinica 12, 387–407.Google Scholar
Datta, S. (1996) On asymptotic properties of bootstrap for AR(1) processes. Journal of Statistical Planning and Inference 53, 361–374.Google Scholar
Hall, P. & Heyde, C. (1980) Martingale Limit Theory and Its Applications. Academic Press.Google Scholar
Han, C., Phillips, P.C.B., & Sul, D. (2010) Uniform Asymptotic Normality in Stationary and Unit Root Autoregression. Working paper, Yale University.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.Google 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
Mikusheva, A. (2007) Uniform inference in autoregressive models. Econometrica 75, 1411–1452.CrossRefGoogle Scholar
Owen, A. (2001) Empirical Likelihood. Chapman and Hall.Google Scholar
Phillips, P.C.B. (1987) Toward a unified asymptotic theory of autoregression. Biometrika 74, 535–574.Google Scholar
Phillips, P.C.B. (1990) Time series regression with a unit-root and infinite-variance errors. Econometric Theory 6, 44–62.Google Scholar
Phillips, P.C.B. & Han, C. (2008) Gaussian inference in AR(1) time series with or without a unit root. Econometric Theory 63, 1023–1078.Google Scholar
Qin, J. & Lawless, J. (1994) Empirical likelihood and general estimating equations. Annals of Statistics 22, 300–325.Google Scholar
So, B.S. & Shin, D.W. (1999) Cauchy estimators for autoregressive processes with applications to unit root tests and confidence intervals. Econometric Theory 15, 165–176.Google Scholar