| Popis: |
Modelling high-dimensional volatilities is a challenging topic, especially for high-dimensional discrete-valued time series data. This paper proposes a threshold spatial GARCH-type model for high-dimensional count data with network structure. The proposed model can simplify the parameterization by taking use of the network structure in data, and can capture the asymmetry in dynamics of volatilities by adopting a threshold structure. Our model is called Poisson Threshold Network GARCH model, because the conditional distributions are assumed to be Poisson distribution. Asymptotic theory of our maximum-likelihood-estimator (MLE) for the proposed spatial model is derived when both sample size and network dimension go to infinity. We get asymptotic statistical inferences via investigating the week dependence among components of the model and using limit theorems for weekly dependent random fields. Simulations are conducted to test the theoretical results, and the model is fitted to real count data as illustration of the proposed methodology. |
