  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.

Methodology