Patrick Aschermayr, Konstantinos Kalogeropoulos
arXiv 25 Jan 2023 · Statistics — Applications
arXiv:2301.10494 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. HSMMs are typically used less frequently than their basic HMM counterpart due to the increased computational challenges when evaluating the likelihood function. Moreover, while both models are sequential in nature, parameter estimation is mainly conducted via batch estimation methods. Thus, a major motivation of this paper is to provide methods to estimate HSMMs (1) in a computationally feasible time, (2) in an exact manner, i.e. only subject to Monte Carlo error, and (3) in a sequential setting. We provide and verify an efficient computational scheme for Bayesian parameter estimation on HSMMs. Additionally, we explore the performance of HSMMs on the VIX time series using Autoregressive (AR) models with hidden semi-Markov states and demonstrate how this algorithm can be used for regime switching, model selection and clustering purposes.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | C. Andrieu, A. Doucet, and R. Holenstein (2010) Particle markov chain monte carlo methods | 1.000 | 5 | 3 | 100% |
| 2 | M. Dewar, C. Wiggins, and F. Wood (2012) Inference in hidden markov models with explicit state duration distributions | 0.843 | 3 | 3 | 100% |
| 3 | Gregor Kastner (2016) Dealing with stochastic volatility in time series using the r package stochvol | 0.737 | 3 | 2 | 100% |
| 4 | Kevin Murphy (2002) Hidden semi-markov models (hsmms), 01 2002 | 0.737 | 3 | 2 | 100% |
| 5 | A. Doucet and A. Johansen (2011) A tutorial on particle filtering and smoothing: Fifteen years later, 2011 | 0.644 | 2 | 2 | 100% |
| 6 | M. J. Johnson and A. S. Willsky (2013) Bayesian nonparametric hidden semi-markov models | 0.644 | 2 | 2 | 100% |
| 7 | S. Yu (2016) Hidden Semi-Markov Models: Theory, Algorithms and Applications | 0.644 | 2 | 2 | 100% |
| 8 | C. Andrieu and G. O. Roberts (2009) The pseudo-marginal approach for efficient monte carlo computations | 0.644 | 2 | 2 | 100% |
| 9 | N Chopin, P E Jacob, and O Papaspiliopoulos (2012) SMC 2: an efficient algorithm for sequential analysis of state space models | 0.644 | 2 | 2 | 100% |
| 10 | Radford M. Neal (2012) Mcmc using hamiltonian dynamics, 2012 | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 48 scored citations.