Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the observation density. The main advantages of the methodology can be summarized as follows: (i) it relaxes the critical assumption of a Gaussian prior distribution for the latent states underlying such approaches; (ii) can be applied to a general class of state-space models including univariate and multivariate location, scale and count data models; (iii) has a very simple structure based on forward-backward recursions similar to the Kalman filter and smoother; (iv) allows a straightforward computation of confidence bands around the state estimates reflecting the combination of parameter and filtering uncertainty. We show through an extensive Monte Carlo study that the mean square loss with respect to exact simulation-based methods is small in a wide range of scenarios. We finally illustrate empirically the application of the methodology to the estimation of stochastic volatility and correlations in financial time-series.

翻译：采用扰动技术，我们推导出一种新的近似滤波与平滑方法论，该方法在多个方向上推广了基于观测密度得分与Hessian矩阵的若干现有鲁棒滤波方法。该方法的主要优势可归纳如下：（i）放宽了此类方法中潜在状态服从高斯先验分布的关键假设；（ii）可应用于包含单变量与多变量位置、尺度及计数数据模型的广义状态空间模型类；（iii）具有基于前向-后向递归的极简结构，类似于卡尔曼滤波与平滑器；（iv）允许直接计算反映参数与滤波不确定性组合的状态估计置信带。通过广泛的蒙特卡洛研究，我们证明在广泛场景下，该方法相对于精确仿真方法的均方损失较小。最后，我们通过实证展示了该方法在金融时间序列中随机波动率与相关性估计的应用。