Non-homogeneous Hidden Markov Model Research Articles

Potential climate predictability of renewable energy supply and demand for Texas given the ENSO hidden state.

Climate variability influences renewable electricity supply and demand and hence system reliability. Using the hidden states of the sea surface temperature of tropical Pacific Ocean that reflect El Niño-Southern Oscillation (ENSO) dynamics that is objectively identified by a nonhomogeneous hidden Markov model, we provide a first example of the potential predictability of monthly wind and solar energy and heating and cooling energy demand for 1 to 6 months ahead for Texas, United States, a region that has a high penetration of renewable electricity and is susceptible to disruption by climate-driven supply-demand imbalances. We find a statistically significant potential for oversupply or undersupply of energy and anomalous heating/cooling demand depending on the ENSO state and the calendar month. Implications for financial securitization and the potential application of forecasts are discussed.

A predictor-informed multi-subject bayesian approach for dynamic functional connectivity.

Dynamic functional connectivity investigates how the interactions among brain regions vary over the course of an fMRI experiment. Such transitions between different individual connectivity states can be modulated by changes in underlying physiological mechanisms that drive functional network dynamics, e.g., changes in attention or cognitive effort. In this paper, we develop a multi-subject Bayesian framework where the estimation of dynamic functional networks is informed by time-varying exogenous physiological covariates that are simultaneously recorded in each subject during the fMRI experiment. More specifically, we consider a dynamic Gaussian graphical model approach where a non-homogeneous hidden Markov model is employed to classify the fMRI time series into latent neurological states. We assume the state-transition probabilities to vary over time and across subjects as a function of the underlying covariates, allowing for the estimation of recurrent connectivity patterns and the sharing of networks among the subjects. We further assume sparsity in the network structures via shrinkage priors, and achieve edge selection in the estimated graph structures by introducing a multi-comparison procedure for shrinkage-based inferences with Bayesian false discovery rate control. We evaluate the performances of our method vs alternative approaches on synthetic data. We apply our modeling framework on a resting-state experiment where fMRI data have been collected concurrently with pupillometry measurements, as a proxy of cognitive processing, and assess the heterogeneity of the effects of changes in pupil dilation on the subjects' propensity to change connectivity states. The heterogeneity of state occupancy across subjects provides an understanding of the relationship between increased pupil dilation and transitions toward different cognitive states.

FinaleMe: Predicting DNA methylation by the fragmentation patterns of plasma cell-free DNA

Analysis of DNA methylation in cell-free DNA reveals clinically relevant biomarkers but requires specialized protocols such as whole-genome bisulfite sequencing. Meanwhile, millions of cell-free DNA samples are being profiled by whole-genome sequencing. Here, we develop FinaleMe, a non-homogeneous Hidden Markov Model, to predict DNA methylation of cell-free DNA and, therefore, tissues-of-origin, directly from plasma whole-genome sequencing. We validate the performance with 80 pairs of deep and shallow-coverage whole-genome sequencing and whole-genome bisulfite sequencing data.

Some Generalized Entropy Ergodic Theorems for Nonhomogeneous Hidden Markov Models

Entropy measures the randomness or uncertainty of a stochastic process, and the entropy rate refers to the limit of the time average of entropy. The generalized entropy rate in the form of delayed averages can overcome the redundancy of initial information while ensuring stationarity. Therefore, it has better practical value. A Hidden Markov Model (HMM) contains two stochastic processes, a stochastic process in which all states can be observed and a Markov chain in which all states cannot be observed. The entropy rate is an important characteristic of HMMs. The transition matrix of a homogeneous HMM is unique, while a Nonhomogeneous Hidden Markov Model (NHMM) requires the transition matrices to be dependent on time variables. From the perspective of model structure, NHMMs are novel extensions of homogeneous HMMs. In this paper, the concepts of the generalized entropy rate and NHMMs are defined and fully explained, a strong limit theorem and limit properties of a norm are presented, and then generalized entropy ergodic theorems with an almost surely convergence for NHMMs are obtained. These results provide concise formulas for the computation and estimation of the generalized entropy rate for NHMMs.

The predictability of daily rainfall during rainy season over East Asia by a Bayesian nonhomogeneous hidden Markov model

AbstractPrecipitation plays a significant role in human society and the environment, and how large‐scale climatic features influence precipitation has obtained worldwide attention. The nonhomogeneous hidden Markov model (NHMM) is a typical method to downscale large‐scale climatic elements to the regional level for many hydrologic applications. The traditional NHMM using point estimates of parameters has the risk to have no solutions for parameter estimation, but the Bayesian‐NHMM provides a Bayesian method to estimate parameters and avoids the risk. In this study, the suitability of the Bayesian‐NHMM in East Asia is evaluated. Two typical regions (i.e., the Yangtze River basin and the Zhujiang River basin in China) dominated by different climates were chosen to check model performance. Results show that: (1) the model could divide rainy‐season precipitation into several hidden states, whose variation is correspondent to the variability of monsoon and flux moisture transportation; (2) the model captures seasonality and inter‐annual variation of precipitation amount and also wet days during rainy season well in both river basins. These results suggest that the model could improve the prediction of daily precipitation in East Asia, which in turn could help many regions with similar climatic conditions worldwide to supervise floods and droughts.

A stacked ensemble learning and non‐homogeneous hidden Markov model for daily precipitation downscaling and projection

AbstractGlobal circulation models (GCMs) are routinely used to project future climate conditions worldwide, such as temperature and precipitation. However, inputs with a finer resolution are required to drive impact‐related models at local scales. The non‐homogeneous hidden Markov model (NHMM) is a widely used algorithm for the precipitation statistical downscaling for GCMs. To improve the accuracy of the traditional NHMM in reproducing spatiotemporal precipitation features of specific geographic sites, especially extreme precipitation, we developed a new precipitation downscaling framework. This hierarchical model includes two levels: (1) establishing an ensemble learning model to predict the occurrence probabilities for different levels of daily precipitation aggregated at multiple sites and (2) constructing a NHMM downscaling scheme of daily amount at the scale of a single rain gauge using the outputs of ensemble learning model as predictors. As the results obtained for the case study in the central‐eastern China (CEC), show that our downscaling model is highly efficient and performs better than the NHMM in simulating precipitation variability and extreme precipitation. Finally, our projections indicate that CEC may experience increased precipitation in the future. Compared with ~26 years (1990–2015), the extreme precipitation frequency and amount would significantly increase by 21.9%–48.1% and 12.3%–38.3%, respectively, by the late century (2075–2100) under the Shared Socioeconomic Pathway 585 climate scenario.

Modeling three-dimensional T-cell motility using clustering and hidden Markov models.

Recent advances in imaging technologies now allow for real-time tracking of fast-moving immune cells as they search for targets such as pathogens and tumor cells through complex three-dimensional tissues. Cytotoxic T cells are specialized immune cells that continually scan tissues for such targets to engage and kill, and have emerged as the principle mediators of breakthrough immunotherapies against cancers. Modeling the way these T cells move is of great value in furthering our understanding of their collective search efficiency. T-cell motility is characterized by heterogeneity at two levels: (a) Individual cells display different distributions of translational speeds and turning angles, and (b) each cell can during a given track, its motility, switch between local search and directional motion. Despite a likely considerable influence on a motile population's search performance, statistical models that accurately capture both such heterogeneities in a distinguishing manner are lacking. Here, we model three-dimensional T-cell trajectories through a spherical representation of their incremental steps and compare model outputs to real-world motility data from primary T cells navigating physiological environments. T cells in a population are clustered based on their directional persistence and characteristic "step lengths" therein capturing between-cell heterogeneity. The motility dynamics of cells within each cluster are individually modeled through hidden Markov model to capture within-cell transitions between local and more extensive search patterns. We explore the importance of explicitly capturing altered motility patterns when cells lie in close proximity to one another, through a non-homogenous hidden Markov model.

Adaptive Fuzzy Asynchronous Control for Nonhomogeneous Markov Jump Power Systems Under Hybrid Attacks

This article investigates the adaptive fuzzy asynchronous control problem for discrete-time nonhomogeneous Markov jump power systems under hybrid attacks. A nonhomogeneous Markov process is used to describe the phenomenon of transient failures occurring in power lines and subsequent switching of associated circuit breakers. The corresponding nonhomogeneous hidden Markov model is utilized to detect the jump modes of power systems. Both deception attack and denial-of-service attack are analyzed simultaneously owing to the vulnerability of power systems. With detected modes and fuzzy logic systems, an adaptive fuzzy asynchronous control strategy is proposed. Using the mode-dependent Lyapunov function, the existence conditions of the desired controller law are obtained such that the closed-loop power systems are bounded stable in the mean-square sense. Finally, the usefulness of the developed control strategy is demonstrated by a numerical example.

Analyzing the Rainfall Pattern in Honduras Through Non-Homogeneous Hidden Markov Models

One of the major climatic interests of the last decades has been to understand and describe the rainfall patterns of specific areas of the world as functions of other climate covariates. We do it for the historical climate monitoring data from Tegucigalpa, Honduras, using non-homogeneous hidden Markov models (NHMMs), which are dynamic models usually used to identify and predict heterogeneous regimes. For estimating the NHMM in an efficient and scalable way, we propose the stochastic Expectation-Maximization (EM) algorithm and a Bayesian method, and compare their performance in synthetic data. Although these methodologies have already been used for estimating several other statistical models, it is not the case of NHMMs which are still widely fitted by the traditional EM algorithm. We observe that, under tested conditions, the performance of the Bayesian and stochastic EM algorithms is similar and discuss their slight differences. Analyzing the Honduras rainfall data set, we identify three heterogeneous rainfall periods and select temperature and humidity as relevant covariates for explaining the dynamic relation among these periods.

Estimating multisite precipitation by a stepwise NHMM-VAR model considering the spatiotemporal correlations of precipitation amounts

• This study developed a stepwise NHMM-VAR multisite downscaling model. • The NHMM-VAR model performs well not only in modeling the statistical properties but also in reproducing the spatiotemporal correlations of multisite precipitation amounts. • The temporal intermittency of precipitation amounts is considered in the NHMM-VAR model. The nonhomogeneous hidden Markov model (NHMM) is a popular statistical downscaling (SD) approach that can be used for multisite precipitation estimation. However, the NHMM assumes that once the days with the occurrence of precipitation have been determined, the precipitation amounts at each station on wet days can be conditionally independently generated from a parametric family of probability distribution functions without considering impacts from the past precipitation amounts and the neighboring stations. Such assumptions may lead to underestimation of the spatiotemporal correlations (i.e., temporal autocorrelation and spatial cross-correlations) of actual multisite precipitation amounts. Thus, this study developed a stepwise downscaling method called the nonhomogeneous hidden Markov model - vector autoregressive (NHMM-VAR), in which the NHMM is used to determine the probabilities for dry days and marginal distributions of multisite daily mean precipitation amounts on wet days based on the large-scale atmospheric covariates, then a VAR(1) model is used to reproduce the spatiotemporal correlations of actual multisite daily mean precipitation amounts. A comparison experiment between the NHMM and the NHMM-VAR models is conducted against outputs from eight global climate models (GCMs) of Phase 6 of the Coupled Model Intercomparison Project (CMIP6) over the Pearl River basin (PRB) of South China. The results show that the NHMM-VAR model performs well not only in modeling the statistical properties but also in reproducing the spatiotemporal correlations of actual multisite daily mean precipitation amounts, which indicates that the VAR model does add value to the NHMM downscaling method.

Peak-to-peak fuzzy filtering of nonlinear discrete-time systems with markov communication protocol

This study deals with the peak-to-peak fuzzy filtering problem for a class of nonlinear discrete-time systems with analog fading channels and communication protocol, in which the nonlinear system is modeled by the Takagi-Sugeno fuzzy model. In analog fading channels, a homogeneous Markov chain is forwarded to model the random time-varying amplitude attenuation. Aiming at alleviating the utilization of energy consumption and preventing data collision/congestion in constraint networks, a Markov communication protocol is exploited to orchestrate the data transmission, in which only one sensor can get permission to release the measurement during each time interval. In virtue of the merging strategy, a new joint Markov chain is presented to incorporate the fading channels and the communication protocol. Differently, in order to eliminate the obstacle of design conservatism, a novel peak-to-peak filter design methodology is developed, whose asynchronization is described by a nonhomogeneous hidden Markov model. Under the aforementioned framework, the resulting system is stochastically stable with a desired peak-to-peak performance index. To this end, a practical example is addressed to indicate the validity and applicability of the presented peak-to-peak filter design strategy.

Understanding the merging behavior patterns and evolutionary mechanism at freeway on-Ramps

Understanding human merging behavior patterns at freeway on-ramps is important for assisting the decisions of autonomous driving. This study develops a primitive-based framework to identify the driving patterns during merging processes and reveal the evolutionary mechanism in congested traffic flow at freeway on-ramps. The Nonhomogeneous Hidden Markov Model is introduced to decompose the merging processes into primitives containing semantic information. Then, the time-series K-means clustering is used to group these primitives with variable-length time series into interpretable merging behavior patterns. Different from traditional state segmentation methods (e.g. Hidden Markov Model), the model proposed in this study considers the dependence of transition probability on exogenous variables, thereby revealing the influence of covariates on the evolution of driving patterns. This approach is evaluated in the merging area at a freeway on-ramp using the INTERACTION dataset. Results demonstrate that the proposed approach can deeply analzye the complicated merging processes and provide interpretable merging behavior patterns as well as the evolutionary mechanism. The findings in this study can be useful for designing and improving the merging decision-making of autonomous vehicles.

Increase of Future Summer Rainfall in the Middle and Lower Reach of the Yangtze River Basin Projected With a Nonhomogeneous Hidden Markov Model

AbstractAmong the statistical downscaling tools available for regional climate simulation, the nonhomogeneous hidden Markov model (NHMM) is a powerful and efficient algorithm. It consists of establishing statistical relations between predictand and predictors through a hidden layer of Markov process and a covariate nonhomogeneous term as external forcing. Here, it is used to simulate summer daily precipitation in the middle and lower reach of the Yangtze River basin (MLYRB), including future projection. Results show that NHMM well identifies large‐scale circulation features that are physically consistent with regional rainfall patterns. MLYRB exhibits a general wetness for 1.5°C and 2°C global warming targets, with smaller (larger) increase for the west (east). Such changes correspond to increases in the occurrence frequency of synoptic weather patterns with stronger and more westward Western Pacific Subtropical High and stronger westerly jet. This contributes to moistening MLYRB with increasing occurrence frequency for those wetter rainfall patterns.

Relationships between Large-Scale Climate Signals and Winter Precipitation Amounts and Patterns over Iran

Precipitation is one of the most complex weather phenomena; its successful spatiotemporal modeling provides substantial information for designing water management systems. This research aimed to determine the relationship of sixteen large-scale climate signals with weather types (WTs) as well as precipitation amounts over Iran during the winter season (January–March). Daily precipitation data covering the period 1991–2010 were collected from 130 weather stations across the country. In addition, four atmospheric variables affecting the precipitation process over Iran were derived from National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis datasets as predictors. Several nonhomogeneous hidden Markov models (NHMMs) were employed to identify the prevailing WTs governing the spatial distributions of daily precipitation in winter over Iran. A hidden state (i.e., WTs) in NHMMs was dependent on an immediately previous state of WT in the hidden layer and the reanalyzed atmospheric variables at the current time in the predictor layer. Daily WTs over the recording period were decoded using Viterbi’s algorithm. Results showed that the NHMM including the atmospheric variable of mean sea level pressure (Mslp) in the predictor layer had the minimum value (= 0) of Bayesian information criterion difference (BICD) among the other variables and was treated as the best model. The chosen model distinguished the eight spatially coherent WTs for winter that were in accordance with the eight synoptic patterns influencing the study area. Based on the Spearman’s rank method, amounts of winter precipitation at many stations in Iran were significantly correlated with four climate signals, including the atlantic multidecadal oscillation (AMO), East Atlantic/West Russia (EA/WR) pattern, Southern Oscillation Index (SOI), and Trans Polar Index (TPI). However, these station-based relationships could not exhibit well the spatial dependencies of the teleconnections and regional precipitation. It was also found that the unconditional and conditional frequencies of WTs were under the influence of a greater number of large-scale climate signals than the precipitation amounts, were under the influence of a greater number of large-scale climate signals. Moreover, the inherent nature of WTs in keeping spatial dependencies allowed for a better understanding of regional teleconnective relationships. These findings confirmed the advantage of regional rather than local assessments of teleconnective relationships.

ENSO Dynamics, Trends, and Prediction Using Machine Learning

AbstractEl Niño–Southern Oscillation (ENSO) has global effects on the hydrological cycle, agriculture, ecosystems, health, and society. We present a novel nonhomogeneous hidden Markov model (NHMM) for studying the underlying dynamics of sea surface temperature anomalies (SSTA) over the region 15°N–15°S, 150°E–80°W from January 1856 to December 2019, using the monthly SSTA data from the Kaplan extended SST v2 product. This nonparametric machine learning scheme dynamically simulates and predicts the spatiotemporal evolution of ENSO patterns, including their asymmetry, long-term trends, persistence, and seasonal evolution. The model identifies five hidden states whose spatial SSTA patterns are similar to the so-called ENSO flavors in the literature. From the fitted NHMM, the model shows that there are systematic trends in the frequency and persistence of the regimes over the last 160 years that may be related to changes in the mean state of basin temperature and/or global warming. We evaluated the ability of NHMM to make out-of-sample probabilistic predictions of the spatial structure of temperature anomalies for the period 1995–2016 using a training period from January 1856 to December 1994. The results show that NHMMs can simulate the behavior of the Niño-3.4 and Niño-1.2 regions quite well. The NHMM results over this period are comparable or superior to the commonly available ENSO prediction models, with the additional advantage of directly providing insights as to the space patterns, seasonal, and longer-term trends of the SSTA in the equatorial Pacific region.

Downscaling Seasonal Climate Forecasts for Risks Management of Rice Production in the Philippines

Objectives: This study is centered on the potential use of a dynamic seasonal climate forecast for informing climate risk management in Central Luzon, Philippines to improve rice productivity and resilience. Specifically, we seek to test the downscalibility of the seasonal climate forecasts in the region using a multi-variate spatio-temporal downscaling technique, understand and assess the predictability of rice yield at selected growing areas in the Philippines, and provide guidance on how to develop agricultural risk management strategies. Methods/statistical analysis: The coupled Global Circulation Model (GCM) CFSv2 was used to evaluate the utility of MJJA (May-June-JulyAugust) rainfall forecasts for risk management of rice production in Central Luzon, Philippines. We used a non-homogeneous hidden Markov model (NHMM) to downscale and simulate the GCM forecasts to selected weather stations in the region. On the other hand, we evaluated the skill of the climate forecasts for predicting crop yields. The simulated rainfall was used to drive the rice models set up in DSSATv4.5. Other weather variables needed by DSSAT were generated and conditioned on the occurrence of rainfall based on NHMM rainfall simulation. Simulated rice yields obtained from these models using observed (i.e., simulated by observed weather) and conditioned rainfall (i.e., NHMM downscaling) serve as a baseline for evaluating yields. We also performed a sensitivity analysis to assess appropriate planting windows for the target season for risk management. Findings: Inter-annual variability of rainfall is moderately simulated, with a skill (r) of 0.41, suggesting that NHMM was fairly successful downscaling rainfall from the regional scale given the predictive nature of the predictor, at three months lead time. The observed MJJA mean rainfall from the six stations falls at around 56% within the interquartile ranges of simulated rainfall, which indicates reasonable skill of the NHMM downscaling CFSv2’s MJJA rainfall hindcasts. Simulated yield was found comparable with the observed at 5% level of significance using t-test (p > 0.05). The correlations between observed and predicted yields are equal to 0.56. This indicates that the models can represent about 31.36% of the inter-annual variability of the yields of rice, albeit of the three months lead-time of the CFSv2 hindcasts. It suggests a reasonable performance of the models in simulating rice yield using the NHMM generated climate information. Climatologically, the best planting and sowing windows for rice in the study area is on the first week of May. This can be adjusted by using seasonal climate forecasts information. Harvest period should not cross over in the month of September to avoid exposure to heavy typhoons. Application/ improvements: Sensitivity analysis showed that planting rice earlier than the usual planting windows practiced by the farmers could improve resilience to climate risks. Managing the variance of this management window, however, is of paramount importance, which can be informed by skillful climate forecasts. Keywords: Seasonal Climate Forecast, Downscaling, Nonhomogenous Hidden Markov Model, Crop Model, Climate Risks Management, Yield Prediction.

Non-homogeneous hidden Markov model for downscaling of short rains occurrence in Kenya

Non-homogeneous hidden Markov model (NHMM) is applied in modeling of daily rainfall occurrences across 16 synoptic stations in Kenya. The time series of the data sets was during the October–December (OND “short rains”) season from 1979 to 2005. The tool assumes that the diurnal rainfall events at a network of observing stations are influenced by unobserved states, that is, “weather states.” These states’ evolution is modeled based on a first-order Markov criterion with state-to-state transition probabilities conditioned on some atmospheric variable indices. The five states are selected using the Bayes information criterion (BIC). To downscale daily rainfall occurrences across 16 stations, a NHMM employed global circulation model (GCM) projection outputs for daily precipitation and sea surface temperatures during the study period. The interannual variability of the mean GCM simulated precipitation and mean historical stations rainfall depicts a weak correlation though significant at 90% confidence level. Thus, it implies that GCM-NHMM simulations do not simulate the rainfall occurrences well. The consecutive wet spell length between the historical rainfall datasets and GCM-NHMM simulated precipitation for 90-day frequencies shows a strong positive correlation significant at 95% confidence level. The findings from this study reveal that the modeling tool is suitable for statistical downscaling of daily rainfall occurrences at multisite stations network. The statistical inference from the model is applicable for drought/flood preparedness, water resource management, and inputs into crop models.

A parametric empirical Bayes (PEB) approach for estimating maize progress percentage at field scale

The Crop Progress Percentage (CPP) in a given phenology stage reflects growth status in the crop life cycle. Generally, routine field measurements of this variable are missing, hence various alternative approaches have been proposed for its estimation. Hidden Markov Models (HMMs) which follow the Bayesian structure are helpful tools for this aim. In the current study, an approach based on the parametric empirical Bayes (PEB) method is used for more accurate estimation of the maize CPP at field scale. The CPP information recorded in three experiment sites i.e. Karaj, Darab and Zarghan were used to validate the performance of the PEB method and to test the robustness. The PEB method includes a non-homogeneous HMM along with an empirical method based on fitting a gamma probability density function (PDF) on prior probabilities. Temporal sequence of phonological stages is regarded as the hidden layer and temporal sequence of NDVI and AGDD indices as the observable layer. The procedure of CPPs estimation is based on calculation of prior and posterior probabilities and an inverse normalization. The overall RMSE of the non-homogeneous HMM before applying the empirical method was 15.1, 11.5 and 7.8% for Karaj, Darab and Zarghan, respectively. However, it was found that the applied HMM fails to estimate the CPPs of final phenological stages accurately. The averaging process of the prior probabilities does not include the errors produced by factors such as climate variability or farming practices. To overcome these problems, we used an empirical Bayes method to estimate the hyperparameters of a gamma density function which was applied as a prior density. This simple approach to maintain the inter-annual variability due to non physiological factors, made the prior probabilities more flexible. The applied empirical Bayes approach (PEB) had significantly smaller RMSE (8, 7.5 and 6.4%, respectively); especially in final phenological stages, and led to more accurate prediction of the phenological dates. The findings derived by PEB are more consistent with those obtained by HMM when the inter-annual variability, mainly date of sowing, is minimum (Specifically, for Zarghan station). The proposed modified approach can be recommended for use at the field scale and serve as a promising tool especially in the regions which suffer the inter-annual variability.

Bayesian variable selection in non-homogeneous hidden Markov models through an evolutionary Monte Carlo method

Hidden Markov models (HMMs) are dynamic mixture models applied to time series in order to classify the observations into a small number of homogeneous groups, to understand when change points occur, and to model data heterogeneity through the switching between subseries with different state-dependent parameters. In the most general case, HMMs have an unobserved Markov chain whose transition probabilities are time-varying and dependent on exogenous variables through multinomial logit functions. When many covariates are available it is worthwhile selecting the subsets of variables which might affect most each row of the transition matrices. A Bayesian method for the stochastic selection of subsets of covariates is proposed by developing a novel evolutionary Monte Carlo algorithm. The methodology is illustrated and shown to be effective by performing experiments and comparisons on both synthetic data sets and a real multivariate time series with covariates.

Identifying the Effect of Public Holidays on Daily Demand for Gas

Summary To reduce operational costs and to ensure security of supply, gas distribution networks require accurate forecasts of the demand for gas. Among domestic and commercial customers, demand relates primarily to the weather and patterns of life and work. Public holidays have a pronounced effect which often spreads into neighbouring days. We call this spread the ‘proximity effect’. Traditionally, the days over which the proximity effect is felt are prespecified in fixed windows around each holiday, allowing no uncertainty in their identification. We are motivated by an application to modelling daily gas demand in two large British regions. We introduce a novel model which does not fix the days on which the proximity effect is felt. Our approach uses a four-state, non-homogeneous hidden Markov model, with cyclic dynamics, where the classification of days as public holidays is observed, but the assignment of days as ‘pre-holiday’, ‘post-holiday’ or ‘normal’ days is unknown. The number of days to the preceding and succeeding holidays guide transitions between states. We apply Bayesian inference and illustrate the benefit of our modelling approach. A version of the model is now being used by one of the UK's regional distribution networks.