GARCH过程的解析矩
Analytic Moments for GARCH Processes
摘要：
对于一个GJR-GRESS规格与通用的创新分布，我们推导出的前四个条件的时刻，向前和汇总的收益率和方差的解析表达式。对于最常用的GARCH模型，将其作为特例。我们还限制这些时刻的时间范围增加，建立正则性条件的时刻聚合回报收敛到正常的时刻。我们的实证研究产生了很好的近似预测分布从这些分析时刻，从而排除了耗时的模拟的需要。
英文摘要：
For a GJR-GARCH specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moment for the most commonly used GARCH models are stated as special cases. We also the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments. Our empirical study yields excellent approximate predictive distributions from these analytic moments, thus precluding the need for time-consuming simulations.
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