From Multidimensional Ornstein - Uhlenbeck Process to Bayesian Vector Autoregressive Process

Lewis N.K. Mambo

Journal of Mathematics Research, 2024, vol. 15, issue 1, 32

Abstract: The main purpose of this paper is to make the connexion between stochastic analysis, the Bayesian Statistics, and time series analysis for policy analysis. This approach solves the problem of mathematical modelling - the presence of uncertainties in the models and parameters - that reduces the policy analysis and forecasting effectiveness. By using the multiple It\^o integral, the multidimensional Ornstein - Uhlenbeck process can be written as a Vector Autoregressive with lag 1 (VAR(1)) that is the generalization of Vector Autoregressive process. The limit of this approach is in fact it requires the strong foundations of stochastic analysis, the Bayesian Statistics, and time series analysis.

Date: 2024
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