Model-based clustering of diffusion processes with constant volatility coefficients using high-frequency data

Shogo Kusano; Masayuki Uchida

Home/Archive/arXiv

arXiv · 2610.37514

Model-based clustering of diffusion processes with constant volatility coefficients using high-frequency data

Shogo Kusano·Masayuki Uchida

View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper considers model-based clustering of diffusion processes using high-frequency data. We formulate a finite mixture model for diffusion processes and develop a clustering method based on their constant diffusion coefficients. Using a quasi-likelihood, we propose estimators of the number of clusters, the diffusion coefficients and the cluster labels, and establish their consistency and the asymptotic normality of the diffusion coefficient estimators under high-frequency asymptotics with the number of observed processes fixed. Simulation studies are conducted to investigate the finite-sample performance of the proposed method.

Explore related subjects

math.ST stat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Shogo Kusano, Masayuki Uchida. 2026-10-27. Model-based clustering of diffusion processes with constant volatility coefficients using high-frequency data. https://arxiv.org/abs/2610.37514

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

New explanations and inference for least angle regression

Efron et al. (2004) introduced least angle regression (LAR) as an algorithm for linear predictions, intended as an alternative to forward selection with connections to penalized regression. However, LAR has remained somewhat of a "black box," where some basic behavioral properties of LAR output are not well understood, including an appropriate termination point for the algorithm. We provide a novel framework for inference with LAR, which also allows LAR to be understood from new perspectives with several newly developed mathematical properties. The LAR algorithm at a data level can viewed as estimating a population counterpart "path" that organizes a response mean along regressor variables which are ordered according to a decreasing series of population "correlation" parameters; such parameters are shown to have meaningful interpretations for explaining variable contributions whereby zero correlations denote unimportant variables. In the output of LAR, estimates of all non-zero population correlations turn out to have independent normal distributions for use in inference, while estimates of zero-valued population correlations have a certain non-normal joint distribution. These properties help to provide a formal rule for stopping the LAR algorithm. While the standard bootstrap for regression can fail for LAR, a modified bootstrap provides a practical and formally justified tool for interpreting the entrance of variables and quantifying uncertainty in estimation. The LAR inference method is studied through simulation and illustrated with data examples.

math.ST↗

arXiv2026

Parametric Statistical Inference in the Zone of Moderate Deviation Probabilities

A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger distance. The Large Deviation Principle in the moderate deviation probability zone is proven for Bayesian estimators and maximum likelihood estimators. A uniform approximation of the logarithm of the likelihood ratio and Theorem on concentration of the posterior Bayesian measure are also established for the zone of moderate deviation probabilities.

math.ST↗

arXiv2026

Asymptotics and finite sample bounds for prediction and smoothing in Wright-Fisher hidden Markov models

We study signal prediction and smoothing in hidden Markov models whose latent signal is a multi-type Wright-Fisher diffusion and whose discrete-time observations are categorical. We consider a repeated-sampling regime with finitely many inspection times and large within-time samples. Under neutrality and parent-independent mutation, the Bayesian predictive and smoothing laws admit exact representations as mixtures of Dirichlet distributions. We show that the one-step predictive and local smoothing laws converge in total variation to the corresponding Wright-Fisher transition and bridge laws determined by the neighboring population frequencies, thereby justifying plug-in approximations based on empirical proportions. For prediction, we derive explicit finite-sample bounds for this approximation and for bounded predictive functionals such as diversity, together with a finite-sample concentration bound for the marginal smoother. The joint posterior at the inspection times concentrates at the target frequencies and satisfies a Bernstein-von Mises limit with distinct interior and boundary regimes, with Gaussian and Gamma limits on different scales. The results allow arbitrary dependence across inspection times. A key technical ingredient is a fixed-interval tail bound for the coalescent-based dual death process.

math.ST↗