Non-standard inference for augmented double autoregressive models with null volatility coefficients
Abstract
This paper considers an augmented double autoregressive (DAR) model, which allows null volatility coefficients to circumvent the over-parameterization problem in the DAR model. Since the volatility coefficients might be on the boundary, the statistical inference methods based on the Gaussian quasi-maximum likelihood estimation (GQMLE) become non-standard, and their asymptotics require the data to have a finite sixth moment, which narrows applicable scope in studying heavy-tailed data. To overcome this deficiency, this paper develops a systematic statistical inference procedure based on the self-weighted GQMLE for the augmented DAR model. Except for the Lagrange multiplier test statistic, the Wald, quasi-likelihood ratio and portmanteau test statistics are all shown to have non-standard asymptotics. The entire procedure is valid as long as the data is stationary, and its usefulness is illustrated by simulation studies and one real example.
Cite
@article{arxiv.1905.01798,
title = {Non-standard inference for augmented double autoregressive models with null volatility coefficients},
author = {Feiyu Jiang and Dong Li and Ke Zhu},
journal= {arXiv preprint arXiv:1905.01798},
year = {2019}
}