Testing for time‐varying nonlinear dependence structures: Regime‐switching and local Gaussian correlation

Abstract

This paper examines nonlinear and time‐varying dependence structures between a pair of stochastic variables, using a novel approach which combines regime‐switching models and local Gaussian correlation (LGC). We propose an LGC‐based bootstrap test for examining whether the dependence structure between two variables is equal across different regimes. We examine this test in a Monte Carlo study, where it shows good level and power properties. We argue that this approach is more intuitive than competing approaches, typically combining regime‐switching models with copula theory. Furthermore, LGC is a semi‐parametric approach, hence avoids any parametric specification of the dependence structure. We illustrate our approach using financial returns from the US–UK stock markets and the US stock and government bond markets, and provide detailed insight into their dependence structures.