Statistical Causality for Multivariate Nonlinear Time Series via Gaussian Process Models

Abstract The ability to test for statistical causality in linear and nonlinear contexts, stationary or non-stationary settings, identify whether influences trend of volatility forms a particularly important class problems explore multi-modal multivariate processes. In this paper, we develop novel testing frameworks general classes time series models. Our framework accommodates flexible features where may be present either: trend, both structural components the Markov processes under study. addition, accommodate added possibilities such as long memory persistence when applying our semi-parametric approach detection. We design calibration procedure formal detect these relationships through Gaussian process provide generic which can applied wide range problems, including partially observed generalised diffusions demonstrate several illustrative examples that are easily testable study properties inference developed power test, sensitivity robustness. then illustrate method on an interesting real data example from commodity modelling.