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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Model-based Clustering
Diffusion Process
Jump
Time Series Data
Jump-diffusion Process
Bayesian Nonparametrics
Dirichlet Process
Multivariate Time Series
Model
Gibbs Sampler
Nonparametric Methods
Sample Path
Stock Prices
Multivariate Data
Bayesian Methods
Discontinuity
Simulation Study
Clustering
Methodology

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

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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.",
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Efficient and flexible model-based clustering of jumps in diffusion processes. / Kang, Bokgyeong; Park, Taeyoung.

In: Journal of the Korean Statistical Society, Vol. 48, No. 3, 09.2019, p. 439-453.

Research output: Contribution to journalArticle

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