Abstract: 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. Behavior of the log empirical likelihood ratio statistic is considered in nearly nonstationary models to assess the local power of unit root tests and to construct confidence intervals. Resampling methods are proposed to improve the finite-sample performance of empirical likelihood statistics. This paper shows that empirical likelihood methodology compares favorably with existing methods and demonstrates its potential for time series with more general innovation structures.
Key words and phrases: Empirical likelihood, dual likelihood, autoregressive models, unit root tests.