TY - JOUR
T1 - Efficient and flexible model-based clustering of jumps in diffusion processes
AU - Kang, Bokgyeong
AU - Park, Taeyoung
N1 - Publisher Copyright:
© 2019 The Korean Statistical Society
PY - 2019/9
Y1 - 2019/9
N2 - 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.
AB - 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.
KW - Bayesian nonparametric inference
KW - Density estimation
KW - Jump–diffusion process
KW - Nested Dirichlet process mixtures
KW - Partially collapsed Gibbs sampler
UR - http://www.scopus.com/inward/record.url?scp=85066101030&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85066101030&partnerID=8YFLogxK
U2 - 10.1016/j.jkss.2019.05.002
DO - 10.1016/j.jkss.2019.05.002
M3 - Article
AN - SCOPUS:85066101030
SN - 1226-3192
VL - 48
SP - 439
EP - 453
JO - Journal of the Korean Statistical Society
JF - Journal of the Korean Statistical Society
IS - 3
ER -