Bayesian Analysis of High Dimensional Vector Error Correction Model

ArXiv ID: 2312.17061 “View on arXiv”

Authors: Unknown

Abstract

Vector Error Correction Model (VECM) is a classic method to analyse cointegration relationships amongst multivariate non-stationary time series. In this paper, we focus on high dimensional setting and seek for sample-size-efficient methodology to determine the level of cointegration. Our investigation centres at a Bayesian approach to analyse the cointegration matrix, henceforth determining the cointegration rank. We design two algorithms and implement them on simulated examples, yielding promising results particularly when dealing with high number of variables and relatively low number of observations. Furthermore, we extend this methodology to empirically investigate the constituents of the S&P 500 index, where low-volatility portfolios can be found during both in-sample training and out-of-sample testing periods.

Keywords: Vector Error Correction Model (VECM), cointegration, Bayesian inference, high-dimensional data, Equities (S&P 500)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper presents advanced Bayesian theory with complex priors, asymptotic analysis, and multi-step derivations for high-dimensional time series, earning a high math score. It includes empirical validation on S&P 500 data with in-sample and out-of-sample portfolio results, but lacks fully detailed backtesting code or implementation specifics, resulting in moderate empirical rigor.

  flowchart TD
    A["Research Goal<br>Determine cointegration rank in<br>high-dim VECM"] --> B["Data Inputs<br>Simulated & S&P 500 Data"]
    B --> C["Key Methodology<br>Bayesian Inference on<br>Cointegration Matrix"]
    C --> D["Computational Process<br>Two Designed Algorithms<br>(High dim / Low sample)"]
    D --> E["Key Findings<br>Accurate rank detection &<br>Low-volatility portfolios"]