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

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.

Keywords: Empirical likelihood, dual likelihood, autoregressive models, unit root tests

Here is the full postscript text for this technical report. It is 490886 bytes long.