Estimation of Cointegrated Spaces: A Numerical Case Study on Efficiency, Accuracy and Influence of the Model Noise

28 Pages Posted: 16 Feb 2017

See all articles by Maciej Marówka

Maciej Marówka

Imperial College London - Department of Mathematics

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

Nikolas Kantas

Imperial College London

Guillaume Bagnarosa

ESC Rennes School of Business

Date Written: February 15, 2017

Abstract

In this paper we develop an analysis of multivariate time series that exhibit reduced rank cointegration, implying that a lower dimensional linear projection of the process can be obtained in which the projected process becomes stationary. Detection of the rank and basis upon which to project the process for stationarity to hold is a critical problem when working with such settings in practice. There is a range of practice when performing estimation of in such multivariate time series settings. In this paper we provide a review of a few selected different models and estimation techniques for these multivariate time series.

Having presented an overview of important new directions with regard to estimation of cointegration relationships we then turn our attention to the performance of a range of estimation procedures. In particular we design a range of numerical studies in order to assess some of these approaches in terms of efficiency and accuracy. In particular, we study the question related to examining the robustness of these classes of estimation procedure in Bayesian and non-parametric estimation approaches to the influence of the model noise in the estimation of the cointegration space.

In this context we develop a novel Bayesian inference procedure not previously studied in cointegration models to estimate the cointegration space. This is based on a Markov Chain Monte Carlo sampling method, that consists of a novel extension of Hamiltonian and Geodesic Monte Carlo for the present problem. We will illustrate the performance of this method numerically and show that it produces results on par with an efficient Gibbs Sampler.

Keywords: Cointegration, Bayesian, Hamiltonian Monte Carlo

Suggested Citation

Marówka, Maciej and Peters, Gareth and Kantas, Nikolas and Bagnarosa, Guillaume, Estimation of Cointegrated Spaces: A Numerical Case Study on Efficiency, Accuracy and Influence of the Model Noise (February 15, 2017). Available at SSRN: https://ssrn.com/abstract=2918511 or http://dx.doi.org/10.2139/ssrn.2918511

Maciej Marówka

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

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

Nikolas Kantas

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

Guillaume Bagnarosa

ESC Rennes School of Business ( email )

2, RUE ROBERT D'ARBRISSEL
Rennes, 35065
France

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