Locally Adaptive Shrinkage Priors for Trends and Breaks in Count Time Series

TL;DR

This paper introduces the NB-BTF, a hierarchical Bayesian model with adaptive shrinkage priors, for accurately capturing trends and abrupt changes in non-stationary count time series, providing reliable inference and uncertainty quantification.

Contribution

The paper develops the NB-BTF framework, a novel adaptive Bayesian trend filter for integer-valued data, addressing limitations of existing methods in modeling local transient features.

Findings

Outperforms existing trend filtering methods in simulations

Effectively captures non-stationary trends with abrupt changes

Provides credible uncertainty quantification in real data application

Abstract

Non-stationary count time series characterized by features such as abrupt changes and fluctuations about the trend arise in many scientific domains including biophysics, ecology, energy, epidemiology, and social science domains. Current approaches for integer-valued time series lack the flexibility to capture local transient features while more flexible models for continuous data types are inadequate for universal applications to integer-valued responses such as settings with small counts. We present a modeling framework, the negative binomial Bayesian trend filter (NB-BTF), that offers an adaptive model-based solution to capturing multiscale features with valid integer-valued inference for trend filtering. The framework is a hierarchical Bayesian model with a dynamic global-local shrinkage process. The flexibility of the global-local process allows for the necessary local regularization while the temporal dependence induces a locally smooth trend. In simulation, the NB-BTF outperforms a number of alternative trend filtering methods. Then, we demonstrate the method on weekly power outage frequency in Massachusetts townships. Power outage frequency is characterized by a nominal low level with occasional spikes. These illustrations show the estimation of a smooth, non-stationary trend with adequate uncertainty quantification.