Bayesian Cointegrated Vector Autoregression Models Incorporating α-Stable Noise for Inter-Day Price Movements Via Approximate Bayesian Computation

39 Pages Posted: 5 Jun 2017

See all articles by Gareth Peters

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

Balakrishnan Kannan

affiliation not provided to SSRN

Ben Lasscock

affiliation not provided to SSRN

Chris Mellen

affiliation not provided to SSRN

Simon Godsill

University of Cambridge - Department of Engineering

Date Written: 2010

Abstract

We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction model (ECM) framework. This involves developing a novel matrix variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and Alpha-stable errors inter-day in the ECM framework. To achieve this we derive a novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR) representation of Alpha-stable inter-day innovations. These results are generalized to asymmetric models for the innovation noise at inter-day boundaries allowing for skewed Alpha-stable models. Our proposed model and sampling methodology is general, incorporating the current literature on Gaussian models as a special subclass and also allowing for price series level shifts either at random estimated time points or known a priori time points. We focus analysis on regularly observed non-Gaussian level shifts that can have significant effect on estimation performance in statistical models failing to account for such level shifts, such as at the close and open of markets. We compare the estimation accuracy of our model and estimation approach to standard frequentist and Bayesian procedures for CVAR models when non-Gaussian price series level shifts are present in the individual series, such as inter-day boundaries. We fit a bi-variate Alpha-stable model to the inter-day jumps and model the effect of such jumps on estimation of matrix-variate CVAR model parameters using the likelihood based Johansen procedure and a Bayesian estimation. We illustrate our model and the corresponding estimation procedures we develop on both synthetic and actual data.

Keywords: Cointegrated Vector Autoregression, α-stable, Approximate Bayesian Computation

Suggested Citation

Peters, Gareth and Kannan, Balakrishnan and Lasscock, Ben and Mellen, Chris and Godsill, Simon, Bayesian Cointegrated Vector Autoregression Models Incorporating α-Stable Noise for Inter-Day Price Movements Via Approximate Bayesian Computation (2010). Available at SSRN: https://ssrn.com/abstract=2980459 or http://dx.doi.org/10.2139/ssrn.2980459

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

Balakrishnan Kannan

affiliation not provided to SSRN

Ben Lasscock

affiliation not provided to SSRN

Chris Mellen

affiliation not provided to SSRN

Simon Godsill

University of Cambridge - Department of Engineering

Cambridge
United Kingdom

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