Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R

This paper describes the R package mhsmm which implements estimation and prediction methods for hidden Markov and semi-Markov models for multiple observation sequences. Such techniques are of interest when observed data is thought to be dependent on some unobserved (or hidden) state. Hidden Markov models only allow a geometrically distributed sojourn time in a given state, while hidden semi-Markov models extend this by allowing an arbitrary sojourn distribution. We demonstrate the software with simulation examples and an application involving the modelling of the ovarian cycle of dairy cows.

A novel methodology based on hidden semi-Markov model for equipment health assessment

As one of the most important aspects of PHM in many application domains, health monitoring and management could maximize the equipment effectiveness within the allowed health ranges. This paper proposes a novel approach to assess the equipment health based on hidden semi-Markov model (HSMM), which is an extension of HMM and does not follow the unrealistic Markov chain assumption to provide more powerful modeling and analysis capability for real problems. With training the standard health state HSMM model by normal state data, the test data is inputted into the trained model in order to calculate the corresponding relative divergence, which is the deviation extent from the standard health state model. Then we can obtain the health index model for the equipment health monitoring and measurement. Moreover, the proposed HSMM based method is applied to the draught fan and showed to be effective

Statistical identification with hidden Markov models of large order splitting strategies in an equity market

Large trades in a financial market are usually split into smaller parts and traded incrementally over extended periods of time. We address these large trades as hidden orders. In order to identify and characterize hidden orders we fit hidden Markov models to the time series of the sign of the tick by tick inventory variation of market members of the Spanish Stock Exchange. Our methodology probabilistically detects trading sequences, which are characterized by a net majority of buy or sell transactions. We interpret these patches of sequential buying or selling transactions as proxies of the traded hidden orders. We find that the time, volume and number of transactions size distributions of these patches are fat tailed. Long patches are characterized by a high fraction of market orders and a low participation rate, while short patches have a large fraction of limit orders and a high participation rate. We observe the existence of a buy-sell asymmetry in the number, average length, average fraction of market orders and average participation rate of the detected patches. The detected asymmetry is clearly depending on the local market trend. We also compare the hidden Markov models patches with those obtained with the segmentation method used in Vaglica {\it et al.} (2008) and we conclude that the former ones can be interpreted as a partition of the latter ones.Comment: 26 pages, 12 figure

Hidden Semi Markov Models for Multiple Observation Sequences: The mhsmm Package for R

This paper describes the R package mhsmm which implements estimation and prediction methods for hidden Markov and semi-Markov models for multiple observation sequences. Such techniques are of interest when observed data is thought to be dependent on some unobserved (or hidden) state. Hidden Markov models only allow a geometrically distributed sojourn time in a given state, while hidden semi-Markov models extend this by allowing an arbitrary sojourn distribution. We demonstrate the software with simulation examples and an application involving the modelling of the ovarian cycle of dairy cows

Hidden semi-Markov models for rainfall-related insurance claims

We analyze the temporal structure of a novel insurance dataset about home insurance claims related to rainfall-induced damage in Norway, and employ a hidden semi-Markov model to capture the non-Gaussian nature and temporal dynamics of these claims. By exploring a wide range of candidate distributions and evaluating their goodness-of-fit as well as commonly used risk measures, we identify a suitable model for effectively modeling insurance losses stemming from rainfall-related incidents. Our findings highlight the importance of considering the temporal aspects of weather-related insurance claims and demonstrate that the proposed hidden semi-Markov model adeptly captures this feature. Moreover, the model estimates reveal a concerning trend: the risks associated with heavy rain in the context of home insurance have exhibited an upward trajectory between 2004 and 2020, aligning with the evidence of a changing climate. This insight has significant implications for insurance companies, providing them with valuable information for accurate and robust modeling in the face of climate uncertainties. By shedding light on the evolving risks related to heavy rain and their impact on home insurance, our study offers essential insights for insurance companies to adapt their strategies and effectively manage these emerging challenges. It underscores the necessity of incorporating climate change considerations into insurance models and emphasizes the importance of continuously monitoring and reassessing risk levels associated with rainfall-induced damage. Ultimately, our research contributes to the broader understanding of climate risk in the insurance industry and supports the development of resilient and sustainable insurance practices

Decoding the Australian electricity market: new evidence from three-regime hidden semi-Markov model

The hidden semi-Markov model (HSMM) is more flexible than the hidden Markov model (HMM). As an extension of the HMM, the sojourn time distribution in the HSMM can be explicitly specified by any distribution, either nonparametric or parametric, facilitating the modelling for the stylised features of electricity prices, such as the short-lived spike and the time-varying mean. By using a three-regime HSMM, this paper investigates the hidden regimes in five Australian States (Queensland, New South Wales, Victoria, South Australia, and Tasmania), spanning the period from June 8, 2008 to July 3, 2016. Based on the estimation results, we find evidence that the three hidden regimes correspond to a low-price regime, a high-price regime, and a spike regime. Running the decoding algorithm, the analysis systemically finds the timing of the three regimes, and thus, we link the empirical results to the policy changes in the Australian National Electricity Market. We further discuss the contributing factors for the different characteristics of the Australian electricity markets at the state-level

MCMC implementation for Bayesian hidden semi-Markov models with illustrative applications

Copyright © Springer 2013. The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-013-9399-zHidden Markov models (HMMs) are flexible, well established models useful in a diverse range of applications. However, one potential limitation of such models lies in their inability to explicitly structure the holding times of each hidden state. Hidden semi-Markov models (HSMMs) are more useful in the latter respect as they incorporate additional temporal structure by explicit modelling of the holding times. However, HSMMs have generally received less attention in the literature, mainly due to their intensive computational requirements. Here a Bayesian implementation of HSMMs is presented. Recursive algorithms are proposed in conjunction with Metropolis-Hastings in such a way as to avoid sampling from the distribution of the hidden state sequence in the MCMC sampler. This provides a computationally tractable estimation framework for HSMMs avoiding the limitations associated with the conventional EM algorithm regarding model flexibility. Performance of the proposed implementation is demonstrated through simulation experiments as well as an illustrative application relating to recurrent failures in a network of underground water pipes where random effects are also included into the HSMM to allow for pipe heterogeneity