Adjusted Empirical Likelihood for Time Series Models

TL;DR

This paper introduces an adjusted empirical likelihood method for stationary time series that ensures solvability of the optimization problem and improves coverage probabilities, especially in small samples.

Contribution

It proposes a modified empirical likelihood ratio statistic that guarantees solutions and retains asymptotic properties, addressing computational issues in previous methods.

Findings

Adjusted method improves coverage probabilities in simulations

Guarantees existence of solutions in empirical likelihood calculations

Performs better than Monti's original method for small samples

Abstract

Empirical likelihood method has been applied to dependent observations by Monti (1997) through the Whittle's estimation method. Similar asymptotic distribution of the empirical likelihood ratio statistic for stationary time series has been derived to construct the confidence regions for the parameters. However, required numerical problem of computing profile empirical likelihood function which involves constrained maximization has no solution sometimes, which leads to the drawbacks of using the original version of the empirical likelihood ratio. In this paper, we propose an adjusted empirical likelihood ratio statistic to modify the one proposed by Monti so that it guarantees the existence of the solution of the required maximization problem, while maintaining the similar asymptotic properties as Monti obtained. Simulations have been conducted to illustrate the coverage probabilities obtained by the adjusted version for different time series models which are better than the ones obtained by Monti's version, especially for small sample sizes.