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

Bokgyeong Kang, Taeyoung Park

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)439-453
Number of pages15
JournalJournal of the Korean Statistical Society
Volume48
Issue number3
DOIs
Publication statusPublished - 2019 Sep

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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