Empirical likelihood for autoregressive models, with applications to unstable time series. (English) Zbl 0998.62075

Summary: 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 emipirical 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.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
62M07 Non-Markovian processes: hypothesis testing