Statistical Causality for Multivariate Non-Linear Time Series via Gaussian Processes

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