# Learning a latent pattern of heterogeneity in the innovation rates of a time series of counts

## TL;DR

This paper introduces a Bayesian hierarchical semiparametric model that learns latent heterogeneity patterns in count time series, improving probabilistic forecasting, demonstrated through crime data analysis.

## Contribution

It presents a novel model that captures heterogeneity in innovation rates of count time series using a Dirichlet process, enhancing forecasting accuracy.

## Key findings

- Model effectively learns latent heterogeneity patterns.
- Favorable results in crime data forecasting.
- Demonstrates improved probabilistic predictions.

## Abstract

We develop a Bayesian hierarchical semiparametric model for phenomena related to time series of counts. The main feature of the model is its capability to learn a latent pattern of heterogeneity in the distribution of the process innovation rates, which are softly clustered through time with the help of a Dirichlet process placed at the top of the model hierarchy. The probabilistic forecasting capabilities of the model are put to test in the analysis of crime data in Pittsburgh, with favorable results.