The Count Time Series Model: Exploring Poisson Hidden Markov Models

The Count Time Series Model: Exploring Poisson Hidden Markov Models

Introduction:

Introduction:

The HMM procedure in SAS Viya has added a new feature called Poisson HMM in its latest release. This feature is designed to handle count time series, which is typically ill-suited for traditional time series analysis techniques. Count time series often present unique challenges for organizations, as they assume that the events occur independently and at a constant rate. However, in reality, the occurrence of an event at one point in time may be related to the occurrence at another point, and the rates can vary over time.

To address these challenges, the Poisson HMM in SAS Viya offers a powerful solution. It allows for modeling different states using distinct Poisson distributions while considering the probability of transitioning between them. This enables organizations to effectively model and forecast count time series by capturing overdispersion and serial dependence in the data.

In this post, we will explore the concept of HMMs and how they can be used to handle count time series. We will also provide a simulated example from the retail industry to demonstrate the effectiveness of the Poisson HMM in analyzing and making inventory plans based on count data. We will discuss the challenges associated with model training and determining the appropriate number of hidden states. Finally, we will showcase the forecasting capabilities of the Poisson HMM by providing one-step forecasts and the expected mean and quantiles of the predicted distribution.

The Poisson HMM is a valuable addition to the SAS Viya platform, offering organizations a robust tool for modeling, analyzing, and forecasting count time series data. By leveraging the power of HMMs, organizations can make more accurate predictions and better informed inventory plans. For more information on HMMs and their applications, visit The HMM Procedure on the SAS website. You can also download the SAS code for the example mentioned in this post from GitLab.

Full Article: The Count Time Series Model: Exploring Poisson Hidden Markov Models

HMM procedure in SAS Viya Supports Hidden Markov Models and More

SAS Viya’s HMM procedure now supports hidden Markov models (HMMs) and other models embedded with HMM. In addition to the finite HMM, there are various models available such as Poisson HMM, Gaussian HMM, Gaussian mixture HMM, regime-switching regression model, and regime-switching autoregression model. This post focuses on the latest addition to PROC HMM in the SAS Viya 2023.03 release, the Poisson HMM.

Count Time Series and the Challenges in Traditional Analysis Techniques

Count time series data pose unique challenges for organizations when it comes to modeling and forecasting. Traditional time series analysis techniques assume that the time series values are continuously distributed, which is not suitable for count data. Count time series are characterized by discrete values, and the occurrence of an event at one point in time might be related to the occurrence of an event at another point in time.

Introduction to Hidden Markov Models (HMMs)

Hidden Markov models (HMMs) are a class of models where the distribution that generates an observation is dependent on the state of an underlying, unobserved Markov process. In the context of count time series analysis, HMMs can be a valuable tool to handle overdispersion and serial dependence in the data.

Poisson HMM: Modeling Different States Using Distinct Poisson Distributions

The Poisson HMM is a specific type of HMM that models different states using distinct Poisson distributions while considering the probability of transitioning between them. This makes it an effective solution for modeling and forecasting count time series data. The Poisson distribution assumes that events occur independently of each other and at a constant rate, but in time series data, this assumption might not hold true.

Simulated Example in the Retail Industry

To demonstrate the effectiveness of the Poisson HMM, a simulated example was created in the context of the retail industry. The example involved generating a set of count data that mimicked the demand pattern of a product with a slow-moving inventory. The objective was to analyze the count data and help make inventory plans.

Determining the Number of Hidden States

One of the challenges in model training is determining the appropriate number of hidden states to use in the model. In this study, the Akaike information criterion (AIC) was used to select the optimal model. After comparing AIC values for models with different numbers of states, the model with three hidden states was found to have the smallest AIC value and was considered the most suitable.

Parameter Estimates and Inventory Plans

The parameter estimates for the Poisson HMM with three states revealed the means (lambda) of the Poisson distribution for each state. Categorizing the states as low, normal, and high-demand states in the retail industry can be helpful in making inventory plans.

Forecasting Count Time Series

The HMM procedure can also be used to forecast count time series. The Poisson HMM provides a one-step forecast with probabilities and predicted distribution quantiles. This information can be used to make informed decisions and plan for future inventory needs.

Summary and Further Information

The Poisson HMM is a valuable tool for modeling and forecasting discrete time series data. It can handle overdispersion and serially correlated data, making it suitable for count time series analysis. The HMM procedure in SAS Viya provides powerful techniques for parameter estimation, decoding hidden states, and forecasting the series. For more information and examples on HMMs, visit The HMM Procedure. SAS code for the example discussed in this post can be downloaded from GitLab.

Summary: The Count Time Series Model: Exploring Poisson Hidden Markov Models

The HMM procedure in SAS Viya provides support for hidden Markov models (HMMs) and other models embedded with HMM. The latest addition to PROC HMM in SAS Viya 2023.03 release is the Poisson HMM, which is designed to handle count time series data. This is important because count time series data often presents unique challenges for modeling and forecasting. The Poisson HMM addresses these challenges by modeling different states using distinct Poisson distributions while considering the probability of transitioning between them. In this post, we explain how the Poisson HMM works and demonstrate its effectiveness through a simulated example in the retail industry. The post also discusses the challenges of model training and how the Poisson HMM can be used for forecasting count time series. The HMM procedure in SAS Viya is a powerful tool for modeling and forecasting count time series data, and the Poisson HMM offers a unique approach to handling these types of data. For more information on HMMs and their applications, visit The HMM Procedure.

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