Abstract The APARCH model attempts to capture asymmetric responses of volatility to positive and negative ‘news shocks’ – the phenomenon known as the leverage effect. Despite its potential, the model’s properties have not yet been fully investigated. While the capacity to account for the leverage is clear from the defining structure, little is known how the effect is quantified in terms of the model’s parameters. The same applies to the quantification of heavy-tailedness and dependence. To fill this void, we study the model in further detail. We study conditions of its existence in different metrics and obtain explicit characteristics: skewness, kurtosis, correlations and leverage. Utilizing these results, we analyze the roles of the parameters and discuss statistical inference. We also propose an extension of the model. Through theoretical results we demonstrate that the model can produce heavy-tailed data. We illustrate these properties using S&P500 data and country indices for dominant European economies.

中文翻译：

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APARCH模型中的尾部行为和依存结构

摘要APARCH模型试图捕获波动率对正面和负面“新闻冲击”的不对称响应，这种现象被称为杠杆效应。尽管具有潜力，但尚未对模型的属性进行全面研究。尽管从定义的结构中可以清楚地说明杠杆的能力，但对于如何根据模型的参数量化效果的了解却很少。重尾和依赖的量化也是如此。为了填补这一空白，我们将进一步研究模型。我们以不同的指标研究其存在的条件，并获得明确的特征：偏度，峰度，相关性和杠杆作用。利用这些结果，我们分析了参数的作用并讨论了统计推断。我们还建议对该模型进行扩展。通过理论结果，我们证明该模型可以生成重尾数据。我们使用S＆P500数据和主要欧洲经济体的国家指数来说明这些属性。