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From Exponential to Polynomial: An Exact Filter for High-Dimensional MSM Models

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  • Daniyal Ali Hameedi

Abstract

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.

Suggested Citation

  • Daniyal Ali Hameedi, 2026. "From Exponential to Polynomial: An Exact Filter for High-Dimensional MSM Models," Papers 2608.22864, arXiv.org.
    • Handle: RePEc:arx:papers:2608.22864
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    File URL: https://arxiv.org/pdf/2608.22864
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