A Markov-switching spatio-temporal ARCH model

TL;DR

This paper introduces a Markov-switching spatio-temporal ARCH model to better capture structural breaks and regime changes in financial volatility data, especially across interconnected locations.

Contribution

It extends existing ARCH models by incorporating Markov-switching regimes into a spatial-temporal framework, improving fit and inference of structural breaks.

Findings

Model shows good finite sample properties in simulations.

Applied to 28 stock indices affected by 2015-2016 Chinese crash.

Outperforms one-regime models in fit and regime detection.

Abstract

Stock market indices are volatile by nature, and sudden shocks are known to affect volatility patterns. The autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) models neglect structural breaks triggered by sudden shocks that may lead to an overestimation of persistence, causing an upward bias in the estimates. Different regime-switching models that have abrupt regime-switching governed by a Markov chain were developed to model volatility in financial time series data. Volatility modelling was also extended to spatially interconnected time series, resulting in spatial variants of ARCH models. This inspired us to propose a Markov switching framework of the spatio-temporal log-ARCH model. In this article, we discuss the Markov-switching extension of the model, the estimation procedure and the smooth inferences of the regimes. The Monte-Carlo simulation studies show that the maximum likelihood estimation method for our proposed model has good finite sample properties. The proposed model was applied to 28 stock indices data that were presumably affected by the 2015-2016 Chinese stock market crash. The results showed that our model is a better fit compared to that of the one-regime counterpart. Furthermore, the smoothed inference of the data indicated the approximate periods where structural breaks occurred. This model can capture structural breaks that simultaneously occur in nearby locations.