Volatility, Jumps, and Predictability of Returns: A Sequential Analysis
提出一种结合辅助粒子滤波和马尔可夫链蒙特卡洛的序贯算法，用于估计含杠杆、非恒定条件均值和跳跃的随机波动率模型中的固定参数和潜在动态，并通过模拟和真实数据验证其性能。
In this article we propose a Monte Carlo algorithm for sequential parameter learning for a stochastic volatility model with leverage, nonconstant conditional mean and jumps. We are interested in estimating the time invariant parameters and the nonobservable dynamics involved in the model. Our simple but effective idea relies on the auxiliary particle filter algorithm mixed together with the Markov Chain Monte Carlo (MCMC) methodology. Adding an MCMC step to the auxiliary particle filter prevents numerical degeneracies in the sequential algorithm and allows sequential evaluation of the fixed parameters and the latent processes. Empirical evaluation on simulated and real data is presented to assess the performance of the algorithm. A numerical comparison with a full MCMC procedure is also provided. We also extend our methodology to superposition models in which volatility is obtained by a linear combination of independent processes.