{"ID":5438583,"CreatedAt":"2026-07-01T01:17:58.482524686Z","UpdatedAt":"2026-07-03T01:40:09.565152011Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.31057","arxiv_id":"2606.31057","title":"Two-stage semiparametric inference for regime-switching jump diffusions with unknown Lévy densities","abstract":"We study high-frequency semiparametric inference for ergodic regime-switching jump diffusions whose continuous coefficients are parametric and whose regime-wise Lévy densities are unknown. The motivation is that jumps contaminate increments while their law is itself unknown, making likelihood-based inference circular in switching models. We propose a two-stage procedure. First, small increments are used in a truncated Gaussian quasi-likelihood to estimate the drift and diffusion parameters. Second, large drift-corrected residuals are sorted by regime and smoothed with a kernel, with normalization by empirical regime exposure time, to estimate the Lévy intensity densities on compact sets away from zero. We establish consistency and mixed-rate asymptotic normality for the quasi-maximum likelihood estimator, and derive \\(L^2(B)\\)-convergence rates for the exposure-normalized residual density estimator. Simulations for switching Ornstein--Uhlenbeck models illustrate the finite-sample performance of the method.","short_abstract":"We study high-frequency semiparametric inference for ergodic regime-switching jump diffusions whose continuous coefficients are parametric and whose regime-wise Lévy densities are unknown. The motivation is that jumps contaminate increments while their law is itself unknown, making likelihood-based inference circular i...","url_abs":"https://arxiv.org/abs/2606.31057","url_pdf":"https://arxiv.org/pdf/2606.31057v1","authors":"[\"Yuzhong Cheng\"]","published":"2026-06-30T02:46:47Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[\"Diffusion Model\"]","has_code":false}