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Abstract: This paper develops a matrix-variate adaptive Markov chain Monte Carlo MCMCmethodology for Bayesian Cointegrated Vector Auto Regressions CVAR. Wereplace the popular approach to sampling Bayesian CVAR models, involving griddyGibbs, with an automated efficient alternative, based on the AdaptiveMetropolis algorithm of Roberts and Rosenthal, 2009. Developing the adaptiveMCMC framework for Bayesian CVAR models allows for efficient estimation ofposterior parameters in significantly higher dimensional CVAR series thanpreviously possible with existing griddy Gibbs samplers. For a n-dimensionalCVAR series, the matrix-variate posterior is in dimension $3n^2 + n$, withsignificant correlation present between the blocks of matrix random variables.We also treat the rank of the CVAR model as a random variable and perform jointinference on the rank and model parameters. This is achieved with a Bayesianposterior distribution defined over both the rank and the CVAR modelparameters, and inference is made via Bayes Factor analysis of rank.Practically the adaptive sampler also aids in the development of automatedBayesian cointegration models for algorithmic trading systems consideringinstruments made up of several assets, such as currency baskets. Previously theliterature on financial applications of CVAR trading models typically onlyconsiders pairs trading n=2 due to the computational cost of the griddyGibbs. We are able to extend under our adaptive framework to $n >> 2$ anddemonstrate an example with n = 10, resulting in a posterior distribution withparameters up to dimension 310. By also considering the rank as a randomquantity we can ensure our resulting trading models are able to adjust topotentially time varying market conditions in a coherent statistical framework.



Author: Gareth W. Peters, Balakrishnan Kannan, Ben Lasscock, Chris Mellen

Source: https://arxiv.org/







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