The idea behind the game

A calm average can hide
a volatile system.

Two places can have similar expected outcomes and very different levels of uncertainty. Volatility is the changing magnitude of fluctuations around an expected level. Connections can link those magnitudes, even when the expected outcomes do not move together.

Our research on spatial and spatiotemporal ARCH/GARCH-type models establishes a class of models for dependence in volatility across connected locations and over time. Some formulations connect volatility across places within the same observation period; temporal formulations can also capture persistence and delayed effects.

The lab makes these ideas explorable through simulated behaviour. Change a connection, follow a cluster of high volatility, and compare what happens. These missions illustrate models; they do not establish the effects of real-world interventions.

Volatility has a spatial structure that can itself be modelled.

A little more about the models

The models have a GARCH-like interpretation: local volatility is linked to the magnitude of departures and volatility at connected locations. Simultaneous spatial relationships can involve feedback and must be modelled jointly. The mechanisms differ between formulations.

“Within the same period” describes a statistical relationship. It does not establish causality or physically instantaneous transmission. With simultaneous spatial feedback, the model’s volatility component is generally not identical to the conditional variance obtained by conditioning on all other locations, but it is proportional to the conditional variance.