Latent Gaussian Dynamic Factor Modeling and Forecasting for Multivariate Count Time Series

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.