Empirical Likelihood for an Autoregressive Model with Explanatory Variables

Abstract

In this article, we use the empirical likelihood method to construct the confidence region for parameters in autoregressive model with martingale difference error. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. The simulation results suggest that the empirical likelihood method outperforms the normal approximation based method in terms of coverage probability.

Empirical likelihood inference for threshold autoregressive conditional heteroscedasticity model

“…These attract the attention of statisticians to make inference for all kinds of statistical models using the empirical likelihood method, such as linear regressive model [9][10][11][12][13], generalized linear models [14][15][16][17], and partially linear models [18][19][20][21]. In recent years, empirical likelihood method is also applied to make statistical inference about time series models, such as autoregressive model [22][23][24], random coefficient autoregressive model [25][26][27][28], and integer-valued autoregressive model [29][30][31][32].…”

Empirical Likelihood Inference for First-Order Random Coefficient Integer-Valued Autoregressive Processes

“…These attractive properties have motivated various authors to extend empirical likelihood methodology to other situations. Now, the empirical likelihood methods have been widely applied to the statistical inference of the time series models (see [14][15][16][17][18][19][20][21]).…”