Latent Gaussian dynamic factor modeling and forecasting for multivariate count time series

TL;DR

This paper introduces a new method for estimating and forecasting high-dimensional count time series by modeling them through latent Gaussian factors, using covariance-based estimators, spectral gap analysis, and particle filtering.

Contribution

It develops a novel estimation approach based on second-order properties, establishes theoretical consistency, and proposes new cross-validation schemes for model selection in high-dimensional count time series.

Findings

Consistent covariance matrix estimators for latent Gaussian models.

Effective forecasting using particle-based sequential Monte Carlo methods.

Validation through simulation and real data application.

Abstract

This work considers estimation and forecasting in a multivariate, possibly high-dimensional count time series model constructed from a transformation of a latent Gaussian dynamic factor series. The estimation of the latent model parameters is based on second-order properties of the count and underlying Gaussian time series, yielding estimators of the underlying covariance matrices for which standard principal component analysis applies. Theoretical consistency results are established for the proposed estimation, building on certain concentration results for the models of the type considered. They also involve the memory of the latent Gaussian process, quantified through a spectral gap, shown to be suitably bounded as the model dimension increases, which is of independent interest. In addition, novel cross-validation schemes are suggested for model selection. The forecasting is carried out through a particle-based sequential Monte Carlo, leveraging Kalman filtering techniques. A simulation study and an application are also considered.