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

36 Pages Posted: 18 Jun 2020

See all articles by Anna Zaremba

Anna Zaremba

affiliation not provided to SSRN

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Date Written: May 24, 2020

Abstract

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.

Keywords: statistical causality, Granger causality, Generalised Likelihood Ratio Test, nested models, ARD kernel

Suggested Citation

Zaremba, Anna and Peters, Gareth, Statistical Causality for Multivariate Non-Linear Time Series via Gaussian Processes (May 24, 2020). Available at SSRN: https://ssrn.com/abstract=3609497 or http://dx.doi.org/10.2139/ssrn.3609497

Anna Zaremba

affiliation not provided to SSRN

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

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