Using a perturbation approach, we derive a new approximate filtering and smoothing methodology for a general class of state-space models including univariate and multivariate location, scale, and count data models. The main properties of the methodology can be summarized as follows: (i) it generalizes several existing approaches to robust filtering based on the score and the Hessian matrix of the observation density by relaxing the critical assumption of a Gaussian prior density underlying this class of methods; (ii) has a very simple structure based on forward-backward recursions similar to the Kalman filter and smoother; (iii) 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：基于扰动方法，我们为包含单变量与多变量位置、尺度及计数数据模型在内的一类广义状态空间模型，推导出一种新的近似滤波与平滑方法。该方法的主要特性可总结如下：（i）通过放宽该类方法中基础的高斯先验密度这一关键假设，推广了基于观测密度得分与海森矩阵的多种现有稳健滤波方法；（ii）具有类似卡尔曼滤波与平滑器的前向-后向递归的极简结构；（iii）能够直接计算反映参数不确定性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证明，在多种场景下，该方法相对于基于精确模拟方法均方损失较小。最后，我们通过金融时间序列中随机波动率与相关性的估计，实证展示了该方法的应用。