Latent Gaussian Dynamic Factor Modeling and Forecasting for Multivariate Count Time Series
提出一种将多元计数时间序列通过潜在高斯动态因子模型进行估计和预测的方法，基于二阶性质估计协方差矩阵，并利用粒子滤波和卡尔曼滤波进行预测，适用于高维数据。
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.