Modelling Volatility of Spatio-temporal Integer-valued Data with Network Structure and Asymmetry

TL;DR

This paper introduces a novel spatial threshold GARCH model for integer-valued spatio-temporal data with network structure, capturing asymmetry in volatility and providing asymptotic inference.

Contribution

It develops a new network-structured threshold GARCH model for spatial data, including asymptotic theory for maximum likelihood estimation.

Findings

Model effectively captures asymmetric volatility in spatial data.

Simulation studies validate the model's performance.

Real data application demonstrates practical utility.

Abstract

This paper proposes a spatial threshold GARCH-type model for dynamic spatio-temporal integer-valued data with network structure. The proposed model can simplify the parameterization by using network structure in data, and can capture the asymmetric property in dynamic volatility by adopting a threshold structure. The proposed model assumes the conditional distribution is Poisson distribution. Asymptotic theory of maximum likelihood estimation (MLE) for the spatial model is derived when both sample size and network dimension are large. We obtain asymptotic statistical inferences via investigation of the weak dependence of components of the model and application of limit theorems for weakly dependent random fields. Simulation studies and a real data example are presented to support our methodology.