AI 中文总结
该研究针对高维MSM模型提出了新的贝叶斯滤波器公式，将时间复杂度从$O(D^k)$降至$O(k^D)$，并验证了扇区滤波器的真实值恢复效果优于朴素滤波器。
AI 中文摘要
本文基于似然结构内的现有置换对称性，提出了用于波动率的离散时间马尔可夫转换多重分形（MSM）模型的贝叶斯滤波器的新公式。我们通过解析和实证表明，该公式将时间复杂度从$O(D^k)$降低到$O(k^D)$，从而显著减少了与维度相关的计算瓶颈。我们比较了朴素滤波器和扇区滤波器之间的一致性，发现尽管存在显著分歧，但后者对真实值的恢复似乎优于前者。
英文摘要
In this paper we propose a new formulation of the Bayesian Filter as used in the discrete-time Markov-Switching-Multifractal (MSM) model of volatility based on existing permutation symmetry within the likelihood structure. We show both analytically and empirically that such a formulation leads to a reduction in time complexity from $O(D^k)$ to $O(k^D)$ thereby significantly reducing the computational bottleneck associated with dimensionality. We compare the agreement between the naive and sector filters and find that while there are significant disagreements, the ground-truth recovery of the latter seems to improve on the former.
