Empirical likelihood inference for error density estimators in first-order autoregression models

ABSTRACT

In this paper we apply empirical likelihood method to the error density estimators in first-order autoregressive models under some mild conditions. The log-likelihood ratio statistic is shown to be asymptotically chi-squared distributed at a fixed point. In simulation, we show that the empirical likelihood produces confidence intervals having theoretical coverage accuracy which is better than normal approximation.

KEYWORDS:

• AR(1) model
• Empirical likelihood
• Kernel density estimator
• Residuals

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J02
• 62E20

Funding

Research supported by the foundation of Zhejiang Educational Committee (No. Y201432167).