标题： 连续可逆波动率模型中的参数推断和预测 显示英文标题

标题： Parametric inference and forecasting in continuously invertible volatility models

摘要： 我们引入了连续可逆波动率模型的概念，该概念依赖于某些Lyapunov条件和某些正则性条件。 我们证明，这几乎等价于利用基于SRE的参数推断方法进行波动率预测的能力，如[16]中给出的。 在非常弱的假设下，我们证明了参数推断的一致性和渐近正态性。 基于这种参数估计，给出了波动率的一个自然强一致预测。 我们成功地将这种方法应用于恢复单变量和多变量GARCH型模型以及EGARCH(1,1)模型上的已知结果。 只要模型是可逆的，我们就证明了预测的一致性；只要极限方差存在，就证明了参数推断的渐近正态性。 最后，我们给出了我们在模拟数据和实际数据上的有希望的实证结果。 显示英文摘要

摘要： We introduce the notion of continuously invertible volatility models that relies on some Lyapunov condition and some regularity condition. We show that it is almost equivalent to the ability of the volatilities forecasting using the parametric inference approach based on the SRE given in [16]. Under very weak assumptions, we prove the strong consistency and the asymptotic normality of the parametric inference. Based on this parametric estimation, a natural strongly consistent forecast of the volatility is given. We apply successfully this approach to recover known results on univariate and multivariate GARCH type models and to the EGARCH(1,1) model. We prove the strong consistency of the forecasting as soon as the model is invertible and the asymptotic normality of the parametric inference as soon as the limiting variance exists. Finally, we give some encouraging empirical results of our approach on simulations and real data.