Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models

Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I.

doi:10.1177/0962280218766964

Cited by 10 publications

(3 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…HMMs are stochastic models wherein observations are assumed to follow a mixed distribution but the parameters of the components are governed by a Markov chain that is unobservable. 33 They are regarded as excellent classification models and are widely used for forecasting crude oil prices. We propose HMR based on HM.…”

Section: Hmrmentioning

confidence: 99%

A hybrid crude oil price forecasting framework: Modified ensemble empirical mode decomposition and hidden Markov regression

Lin,

Xie,

Yang

2024

Energy Science & Engineering

View full text Add to dashboard Cite

The considerable influence of crude oil prices on the international economy has motivated numerous scholars to develop various prediction models. Two difficulties are encountered in forecasting. One is that the time series of crude oil prices show massive jumps in high frequency. The other is that the time series of crude oil prices are characterised by nonlinearity, structural breaks and highly volatile states. Therefore, we propose a hybrid model that incorporates the principle of decomposition–integration. Its overall process can be divided into the steps of decomposition and integration. In decomposition step, modified ensemble empirical mode decomposition is used to decompose the data on crude oil prices. Next, K‐means and principal component analysis are utilised to extract the optimal intrinsic mode function (IMF) from diverse frequencies amongst decomposed IMFs. Following decomposition, different forecasting methods are used to match IMFs with various frequencies for prediction. In accordance with structural breaks and the highly volatile states of high‐frequency series, hidden Markov regression is applied to describe predicted values in a probabilistic manner, providing objective interpretation and forecasting. A neural network is taken to predict intermediate‐frequency IMFs by using a fully connected network. Owing to the low frequency and tendency of the residual sequence to be more stable than other frequency sequences, the autoregressive integrated moving average model is applied as the forecasting method for prediction. Finally, all individual predictions for the eventual results are ensembled as final predictions. Results confirm that the proposed model is better than several normal hybrid and single models in terms of prediction accuracy and Diebold–Mariano test results. All results confirm that the newly proposed hybrid model is a promising tool for the analysis and forecasting of crude oil prices.

show abstract

Section: Hmrmentioning

confidence: 99%

A hybrid crude oil price forecasting framework: Modified ensemble empirical mode decomposition and hidden Markov regression

Lin,

Xie,

Yang

2024

Energy Science & Engineering

View full text Add to dashboard Cite

show abstract

“…As already indicated in Section 1, HMMs are frequently applied in these fields. A health‐related example is described by Sebastian et al, 19 where a time series of monthly Vibrio cholerae (VC) counts is modeled by a three‐state Poisson HMM. There, the three states express “mild,” “moderate,” and “severe” VC epidemic, and they are related to climate conditions.…”

Section: Hidden Markov Models and Applicationsmentioning

confidence: 99%

Control charts for monitoring a Poisson hidden Markov process

Ottenstreuer

Weiß

Knoth

2020

Quality & Reliability Eng

View full text Add to dashboard Cite

Monitoring stochastic processes with control charts is the main field of application in statistical process control. For a Poisson hidden Markov model (HMM) as the underlying process, we investigate a Shewhart individuals chart, an ordinary Cumulative Sum (CUSUM) chart, and two different types of log‐likelihood ratio (log‐LR) CUSUM charts. We evaluate and compare the charts' performance by their average run length, computed either by utilizing the Markov chain approach or by simulations. Our performance evaluation includes various out‐of‐control scenarios as well as different levels of dependence within the HMM. It turns out that the ordinary CUSUM chart shows the best overall performance, whereas the other charts' performance strongly depend on the particular out‐of‐control scenario and autocorrelation level, respectively. For illustration, we apply the HMM and the considered charts to a data set about weekly sales counts.

show abstract

“…The GPD is also apt for modelling underdispersed Poisson data. Going by all these details, one can consider GP-HMM as a better option than P-HMM as shown in Sebastian, Jeyaseelan, Jeyaseelan, Anandan, George & Bangdiwala (2019) for count data modelling. However, the idea of using GPD in HMM is not new.…”

Section: Introductionmentioning

confidence: 99%

Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data

George

Jose

2020

Rev. colomb. estad.

Self Cite

View full text Add to dashboard Cite

The most suitable statistical method for explaining serial dependency in time series count data is that based on Hidden Markov Models (HMMs). These models assume that the observations are generated from a finite mixture of distributions governed by the principle of Markov chain (MC). Poisson-Hidden Markov Model (P-HMM) may be the most widely used method for modelling the above said situations. However, in real life scenario, this model cannot be considered as the best choice. Taking this fact into account, we, in this paper, go for Generalised Poisson Distribution (GPD) for modelling count data. This method can rectify the overdispersion and underdispersion in the Poisson model. Here, we develop Generalised Poisson Hidden Markov model (GP-HMM) by combining GPD with HMM for modelling such data. The results of the study on simulated data and an application of real data, monthly cases of Leptospirosis in the state of Kerala in South India, show good convergence properties, proving that the GP-HMM is a better method compared to P-HMM.

show abstract

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models

Cited by 10 publications

References 48 publications

A hybrid crude oil price forecasting framework: Modified ensemble empirical mode decomposition and hidden Markov regression

A hybrid crude oil price forecasting framework: Modified ensemble empirical mode decomposition and hidden Markov regression

Control charts for monitoring a Poisson hidden Markov process

Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data

Contact Info

Product

Resources

About