Statistical Inference for Periodic Asymmetric Power GARCH Models

ABSTRACT In this paper, we study the statistical inference methods for the periodic asymmetric power GARCH model (PAPGARCH), which can simultaneously capture the periodicity of volatility, the clustering effect, and the asymmetry of market responses. We proposed a data‐driven weighted composite quantile regression (WCQR) estimator based on adaptive weights. This estimator improves efficiency by minimizing the asymptotic variance and its consistency and asymptotic normality are proved. To test for the asymmetry of conditional heteroscedasticity, a Wald‐type test statistic is proposed. We derived the limiting distributions under the null hypothesis, alternative hypothesis, and local alternative hypothesis for the proposed Wald‐type asymmetric test. Monte Carlo experiments showed that WCQR performed better than quasi‐maximum likelihood estimation (QMLE) in small samples, and the test results of the proposed Wald‐type asymmetric test were satisfactory. The modeling experiment of the USD/DZD exchange rate demonstrated the effectiveness of this framework.