Abstract In this paper, we set up a generalized periodic asymmetric power GARCH (PAP-GARCH) model whose coefficients, power, and innovation distribution are periodic over time. We first study its properties, such as periodic ergodicity, finiteness of moments and tail behavior of the marginal distributions. Then, we develop an MCMC algorithm, based on the Griddy-Gibbs sampler, under various distributions of the innovation term (Gaussian, Student-t, mixed Gaussian-Student-t). To assess our estimation method we conduct volatility and Value-at-Risk forecasting. Our model is compared against other competing models via the Deviance Information Criterion (DIC). The proposed methodology is applied to simulated and real data.

中文翻译：

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周期性非对称功率 GARCH 模型的贝叶斯分析

摘要 在本文中，我们建立了一个广义周期性非对称功率 GARCH (PAP-GARCH) 模型，其系数、功率和创新分布随时间呈周期性。我们首先研究它的性质，例如周期性遍历性、矩的有限性和边缘分布的尾部行为。然后，我们开发了一种基于 Griddy-Gibbs 采样器的 MCMC 算法，在创新项的各种分布（高斯、学生-t、混合高斯-学生-t）下。为了评估我们的估计方法，我们进行了波动率和风险价值预测。我们的模型通过偏差信息标准 (DIC) 与其他竞争模型进行比较。所提出的方法适用于模拟和真实数据。