This paper proposes an asymmetric functional-coefficient autoregressive conditional heteroscedasticity in mean (ARCH-M) model, which allows for asymmetry in the volatility. The profile likelihood approach is applied to estimate the parametric and nonparametric components. Under some regularity assumptions, we derive asymptotic behavior of the proposed estimator. To avoid model misspecification, the Wald, quasi-likelihood ratio test statistic and generalized likelihood ratio test statistic are put forward to detect ARCH effect, asymmetric effect and goodness-of-fit, respectively. Moreover, their asymptotic distributions are established under both null and alternative hypotheses. Some Monte Carlo simulations are conducted to evaluate the finite sample performance of the proposed estimation methodology and testing procedure. Also, real data sets are analyzed to demonstrate the applications of the proposed model.

中文翻译：

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非对称函数系数 ARCH-M 模型

本文提出了一种非对称函数系数自回归均值条件异方差（ARCH-M）模型，该模型允许波动性的不对称性。应用轮廓似然方法来估计参数和非参数分量。在一些规律性假设下，我们推导出所提出的估计量的渐近行为。为了避免模型错误指定，提出了Wald、准似然比检验统计量和广义似然比检验统计量来分别检测ARCH效应、非对称效应和拟合优度。此外，它们的渐近分布是在零假设和替代假设下建立的。进行一些蒙特卡罗模拟来评估所提出的估计方法和测试程序的有限样本性能。此外，还分析了真实数据集以演示所提出模型的应用。