Dirichlet mixed process integrated Bayesian estimation for individual securities

Abstract

Bayesian nonparametric methods, particularly the Dirichlet process (DP), have gained increasing popularity in both theoretical and applied research, driven by advances in computing power. Traditional Bayesian estimation, which often relies on Gaussian priors, struggles to dynamically integrate evolving prior beliefs into the posterior distribution for decision-making in finance. This study addresses that limitation by modeling daily security price fluctuations using a Dirichlet process mixture (DPM) model. Our results demonstrate the DPM’s effectiveness in identifying the optimal number of clusters within time series data, leading to more accurate density estimation. Unlike kernel methods, the DPM continuously updates the prior density based on observed data, enabling it to better capture the dynamic nature of security prices. This adaptive feature positions the DPM as a superior estimation technique for time series data with complex, multimodal distributions