Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Empirical Likelihood for Autoregressive Models, with Applications to Unstable Time Series

Publication Date

December, 1998

Publication Type

Tech Report


Chin-Shan Chuang and Ngai Hang Chan


Empirical likelihood is developed for autoregressive models with innovations that form a martingale difference sequence. Limiting distributions of the log empirical likelihood ratio statistic for both the stable and unstable cases are established. The local power of the unit root test obtained via empirical likelihood is obtained for the first-order model, and its finite-sample properties are assessed with simulations. A resampling method is proposed to improve the finite-sample performance of the empirical likelihood statistics. The paper shows that empirical likelihood methodology compares favorably with existing methods and demonstrates its potential for time series with more general innovation structures.