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Poisson Hidden Markov Models in SAS

Ji Shen shows off how to perform discrete time series in SAS:

The HMM procedure in SAS Viya supports hidden Markov models (HMMs) and other models embedded with HMM. PROC HMM supports finite HMM, Poisson HMM, Gaussian HMM, Gaussian mixture HMM, the regime-switching regression model, and the regime-switching autoregression model. This post introduces Poisson HMM, the latest addition to PROC HMM in the SAS Viya 2023.03 release.

Count time series is ill-suited for most traditional time series analysis techniques, which assume that the time series values are continuously distributed. This can present unique challenges for organizations that need to model and forecast them. As a popular discrete probability distribution to handle the count time series, the Poisson distribution or the mixed Poisson distribution might not always be suitable. This is because both assume that the events occur independently of each other and at a constant rate. In time series data, however, the occurrence of an event at one point in time might be related to the occurrence of an event at another point in time, and the rates at which events occur might vary over time.

HMM is a valuable tool that can handle overdispersion and serial dependence in the data. This makes it an effective solution for modeling and forecasting count time series. We will explain how the Poisson HMM can handle count time series by modeling different states by using distinct Poisson distributions while considering the probability of transitioning between them.

Read on for an overview of Hidden Markov Models (in general and the Poisson variation in particular) and some of the challenges you can run into when performing this test.