论文标题
隐藏的马尔可夫过程和自适应过滤的波动性估计
Volatility Estimation of Hidden Markov Processes and Adaptive Filtration
论文作者
论文摘要
考虑了观测值中噪声低的随机微分方程的部分观察到的线性高斯系统。内核型估计器用于估计观察过程极限的衍生物的二次变化。然后，该估计器用于非参数估计，对不可观察成分的挥发性的积分不可或缺。在可观察到的成分中漂移以及状态组件的波动率取决于某些未知参数的情况下，该估计值还用于构建替代估计器。然后，这种替代估计器和Fisher得分设备使我们能够引入单步MLE过程和自适应Kalman-Bucy滤波器。
The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. A kernel-type estimators are used for estimation of the quadratic variation of the derivative of the limit of the observed process. Then this estimator is used for nonparametric estimation of the integral of the square of volatility of unobservable component. This estimator is also used for construction of substitution estimators in the case where the drift in observable component and the volatility of the state component depend on some unknown parameter. Then this substitution estimator and Fisher-score device allows us to introduce the One-step MLE-process and adaptive Kalman-Bucy filter.
