High-dimensional latent Gaussian count time series: Concentration results for autocovariances and applications

TL;DR

This paper develops concentration bounds for autocovariance estimators in high-dimensional latent Gaussian count time series models, enabling reliable inference and parameter estimation in complex, dependent count data.

Contribution

It introduces a general framework for modeling count time series via latent Gaussian processes and establishes concentration results for autocovariance estimation in high dimensions.

Findings

Concentration bounds relate observed counts to latent Gaussian autocovariances.

Application to vector autoregression models with sparse parameter estimation.

Framework ensures flexible modeling of dependencies in count time series.

Abstract

This work considers stationary vector count time series models defined via deterministic functions of a latent stationary vector Gaussian series. The construction is very general and ensures a pre-specified marginal distribution for the counts in each dimension, depending on unknown parameters that can be marginally estimated. The vector Gaussian series injects flexibility into the model's temporal and cross-dimensional dependencies, perhaps through a parametric model akin to a vector autoregression. We show that the latent Gaussian model can be estimated by relating the covariances of the counts and the latent Gaussian series. In a possibly high-dimensional setting, concentration bounds are established for the differences between the estimated and true latent Gaussian autocovariances, in terms of those for the observed count series and the estimated marginal parameters. The results are applied to the case where the latent Gaussian series is a vector autoregression, and its parameters are estimated sparsely through a LASSO-type procedure.