Efficient and flexible model-based clustering of jumps in diffusion processes

• Published in: Journal of the Korean Statistical Society Vol. 48; no. 3; pp. 439 - 453
• Main Authors: Kang, Bokgyeong, Park, Taeyoung
• Format: Journal Article
• Language: English
• Published: Singapore Elsevier B.V 01.09.2019; Springer Singapore; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Bayesian nonparametric inference; Density estimation; Jump–diffusion process; Nested Dirichlet process mixtures; Partially collapsed Gibbs sampler; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학; secondary; Density estimation; Bayesian nonparametric inference; Partially collapsed Gibbs sampler; Jump–diffusion process; Nested Dirichlet process mixtures; primary; primary 62F15; Jump-diffusion process; secondary 97K80
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1016/j.jkss.2019.05.002

Jump–diffusion processes involving diffusion processes with discontinuous movements, called jumps, are widely used to model time-series data that commonly exhibit discontinuity in their sample paths. The existing jump–diffusion models have been recently extended to multivariate time-series data. The models are, however, still limited by a single parametric jump-size distribution that is common across different subjects. Such strong parametric assumptions for the shape and structure of a jump-size distribution may be too restrictive and unrealistic for multiple subjects with different characteristics. This paper thus proposes an efficient Bayesian nonparametric method to flexibly model a jump-size distribution while borrowing information across subjects in a clustering procedure using a nested Dirichlet process. For efficient posterior computation, a partially collapsed Gibbs sampler is devised to fit the proposed model. The proposed methodology is illustrated through a simulation study and an application to daily stock price data for companies in the S&P 100 index from June 2007 to June 2017.