An efficient simulation-based methodology is proposed for the rolling window estimation of state space models, called particle rolling Markov chain Monte Carlo (MCMC) with double block sampling. In our method, which is based on Sequential Monte Carlo (SMC), particles are sequentially updated to approximate the posterior distribution for each window by learning new information and discarding old information from observations. Th particles are refreshed with an MCMC algorithm when the importance weights degenerate. To avoid degeneracy, which is crucial for reducing the computation time, we introduce a block sampling scheme and generate multiple candidates by the algorithm based on the conditional SMC. The theoretical discussion shows that the proposed methodology with a nested structure is expressed as SMC sampling for the augmented space to provide the justification. The computational performance is evaluated in illustrative examples, showing that the posterior distributions of the model parameters are accurately estimated. The proofs and additional discussions (algorithms and experimental results) are provided in the Supplementary Material.
翻译:为州空间模型滚动窗口估计提出了一种高效的模拟方法,称为粒子滚动的Markov链Monte Carlo(MCMC),采用双块取样法。在我们的方法中,以“SMC”为基础,通过学习新信息和放弃从观测中获得的旧信息,对每个窗口的后方分布进行顺序更新,以近似于后方分布。当重要重量下降时,微粒用MCMC算法进行刷新。为了避免对缩短计算时间至关重要的退化性,我们引入了块抽样办法,并以有条件的SMC算法生成多个候选方。理论讨论表明,使用嵌套结构的拟议方法表现为“SMC”取样,以提供理由。在示例中评估了计算性性表现,表明模型参数的后方分布得到准确估计。补充材料提供了证据和补充讨论(数值和实验结果)。