标题： 参数推断和连续可逆波动率模型中的预测 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，该概念依赖于某些李雅普诺夫条件和某些正则性条件。 我们表明，这几乎等同于使用基于[16]中给出的SRE的参数推断方法进行波动率预测的能力。 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。 基于此参数估计，给出了一个自然的强一致波动率预测。 我们将这种方法成功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。 我们证明了只要模型是可逆的，预测就具有强一致性，并且只要极限方差存在，参数推断就具有渐近正态性。 最后，我们在模拟数据和实际数据上给出了我们方法的一些有希望的实证结果。 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.