Adaptive Bayesian MCMC and Rank Selection for Cointegrated VAR Models
Summary
The paper develops an adaptive matrix-variate Markov chain Monte Carlo method for Bayesian cointegrated vector autoregressions. It replaces griddy Gibbs sampling with an automated Adaptive Metropolis approach, intended to make posterior estimation practical for higher-dimensional systems with correlated parameter blocks. The model’s cointegration rank is also treated as unknown, allowing joint inference on rank and model parameters through a Bayesian posterior and Bayes factor analysis.
The authors illustrate the method with a ten-variable model, whose posterior parameter dimension reaches 310, and position the approach as a computational foundation for trading systems using multi-asset instruments such as currency baskets. They argue that random-rank inference can accommodate changing market conditions in a coherent statistical framework. The supplied text describes a methodological contribution and an example, but does not provide trading performance, implementation costs, or evidence that rank adaptation improves live strategy results.
Key ideas
- Adaptive Metropolis sampling is proposed as an alternative to griddy Gibbs for Bayesian cointegrated VARs.
- The sampler targets higher-dimensional models with correlated matrix-valued parameter blocks.
- Cointegration rank is modeled as uncertain and inferred jointly with model parameters.
- Bayes factors are used to compare candidate ranks.
- A ten-variable example demonstrates computational scale, but no trading performance evidence is provided.
Tags
Full text
# Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model # Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC) methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We replace the popular approach to sampling Bayesian CVAR models, involving griddy Gibbs, with an automated efficient alternative, based on the Adaptive Metropolis algorithm of Roberts and Rosenthal, (2009). Developing the adaptive MCMC framework for Bayesian CVAR models allows for efficient estimation of posterior parameters in significantly higher dimensional CVAR series than previously possible with existing griddy Gibbs samplers. For a n-dimensional CVAR series, the matrix-variate posterior is in dimension $3n^2 + n$, with significant correlation present between the blocks of matrix random variables. We also treat the rank of the CVAR model as a random variable and perform joint inference on the rank and model parameters. This is achieved with a Bayesian posterior distribution defined over both the rank and the CVAR model parameters, and inference is made via Bayes Factor analysis of rank. Practically the adaptive sampler also aids in the development of automated Bayesian cointegration models for algorithmic trading systems considering instruments made up of several assets, such as currency baskets. Previously the literature on financial applications of CVAR trading models typically only considers pairs trading (n=2) due to the computational cost of the griddy Gibbs. We are able to extend under our adaptive framework to $n >> 2$ and demonstrate an example with n = 10, resulting in a posterior distribution with parameters up to dimension 310. By also considering the rank as a random quantity we can ensure our resulting trading models are able to adjust to potentially time varying market conditions in a coherent statistical framework.
Shown in full with attribution under the source's licence. Licence: abstract CC0
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.