Title: Framework for detecting statistical causality in warped Gaussian processes
Authors: Anna Zaremba - University College London (United Kingdom) [presenting]
Gareth Peters - University College London (United Kingdom)
Abstract: A new framework is proposed for detecting statistical causality. The challenge in identification and detection of causality in multivariate, non-linear, non-Guassian time series that exhibit non-linear dependence is not trivial. Consequently, models that would allow for structural properties like: non-stationarity, heteroscedasticity, tail dependence, long memory, are rarely studied, especially in the context of statistical causality testing and inference. Gaussian processes are a flexible class of models that can be used to semi-parametrically model time series observations and can incorporate different structural properties. We consider deformations of Gaussian processes, sometimes referred to as warped Gaussian processes, that are specifically designed in this context to capture multivariate dependence and concordance relationships that, when not included in the time series data model, may obfuscate the ability to detect linear and non-linear causal relationships between each marginal time series in the drift or volatility. Testing is performed using the generalised likelihood ratio test (GLRT), and under the assumptions of nested models, where the null hypothesis is the one of lack of causality. We describe ways of constructing such tests to be applicable for a wide range of data structures.