arXiv subjects

Yuzhong Cheng

Publications and source records attributed to Yuzhong Cheng.

8 recordsLinked to original sources

arXiv2026

Tail-corrected semiparametric inference for regime-switching jump diffusions

Regime-switching jump diffusions describe continuous-time dynamical systems that exhibit both abrupt jumps and changes in regime, with applications in economics, ecology, and physics. Statistical inference for such processes is complicated by the interaction between jumps and regime switching. We study an ergodic jump diffusion with exogenous finite-state regime switching. From discrete observations of both the state and regime processes, the estimation targets are the drift and diffusion parameters and the unknown regime-wise Lévy densities, in settings with either finite-variation jumps or locally stable infinite-variation jumps. We first estimate the tail means and coefficient parameters. For finite-variation jumps, coefficient estimation is based on a Gaussian quasi-likelihood; for locally stable infinite-variation jumps with common $1<β<8/5$, diffusion estimation uses a two-step debiasing of truncated realized variation. We then use drift-corrected detected residuals to estimate each Lévy density away from zero. We establish consistency and asymptotic normality for the coefficient estimators, together with an $L^2(B)$-convergence rate for the density estimators. Tail-mean estimation contributes an explicit Lévy-measure term to the drift covariance, whereas the diffusion block retains the Gaussian quasi-score covariance. Simulations illustrate the finite-sample performance of the estimators.

math.ST↗

arXiv2026

Nonparametric Inference for Semigroup Blocks of Switching Diffusions

Regime-conditioned transition probabilities and moments are basic inputs for prediction and decision making in hybrid systems, but their short-time infinitesimal structure is not directly observable. We study nonparametric estimation of regime-indexed semigroup blocks for switching diffusions observed together with their regimes. A Dynkin--Taylor expansion identifies the first two block-generator coefficients, and localized probes recover switching intensities, drift, and diffusion. Under shrinking meshes, a common-design difference cancels the localized level and yields a martingale array; nonoverlapping second differences preserve within-block covariance and produce the variance factor two. The resulting first- and second-order estimators are asymptotically normal, admit feasible studentization, and support short-horizon approximation and specification checks for interactions among primitive coefficients. Fixed-mesh local-polynomial theory and a numerical study complement the recovery results.

math.ST↗

arXiv2026

Ergodicity and High-Frequency Inference for Hybrid Switching Lévy-Driven Stochastic Differential Equations

Hybrid switching Lévy-driven stochastic differential equations with pure-jump noise and state-dependent switching rates are studied under high-frequency observation. A three-stage inference procedure is proposed for the drift, scale, and switching-rate parameters, combining a staged Gaussian quasi-likelihood with an intensity-type contrast. Checkable sufficient conditions for weighted exponential ergodicity are established for the hybrid process; the proof does not rely on Brownian smoothing, but uses a fixed skeleton-chain argument combining small-jump accessibility and regime connectivity. Under ergodicity and the high-frequency sampling scheme, consistency, joint asymptotic normality, and a polynomial-type large deviation inequality are proved for the full estimator. The joint limit exhibits a transparent covariance structure: the drift and scale blocks are coupled through the third moment of the driving Lévy noise, whereas the switching-rate block is asymptotically uncorrelated with the continuous-coefficient blocks. Numerical experiments for models driven by normal inverse Gaussian noise illustrate the finite-sample behavior of the proposed estimators.

math.ST↗

arXiv2025

Statistical inference for ergodic diffusion with Markovian switching

This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the unknown parameters contained in the drift and diffusion coefficients and present a consistent explicit estimator for the generator of the Markov chain. Simulation experiments are conducted to illustrate the theoretical results obtained.

math.ST↗

arXiv2024

Quasi-likelihood-based EM algorithm for regime-switching SDE

This paper considers estimating the parameters in a regime-switching stochastic differential equation(SDE) driven by Normal Inverse Gaussian(NIG) noise. The model under consideration incorporates a continuous-time finite state Markov chain to capture regime changes, enabling a more realistic representation of evolving market conditions or environmental factors. Although the continuous dynamics are typically observable, the hidden nature of the Markov chain introduces significant complexity, rendering standard likelihood-based methods less effective. To address these challenges, we propose an estimation algorithm designed for discrete, high-frequency observations, even when the Markov chain is not directly observed. Our approach integrates the Expectation-Maximization (EM) algorithm, which iteratively refines parameter estimates in the presence of latent variables, with a quasi-likelihood method adapted to NIG noise. Notably, this method can simultaneously estimate parameters within both the SDE coefficients and the driving noise. Simulation results are provided to evaluate the performance of the algorithm. These experiments demonstrate that the proposed method provides reasonable estimation under challenging conditions.

stat.CO↗

arXiv2024

Deep learning-based method for weather forecasting: A case study in Itoshima

Accurate weather forecasting is of paramount importance for a wide range of practical applications, drawing substantial scientific and societal interest. However, the intricacies of weather systems pose substantial challenges to accurate predictions. This research introduces a multilayer perceptron model tailored for weather forecasting in Itoshima, Kyushu, Japan. Our meticulously designed architecture demonstrates superior performance compared to existing models, surpassing benchmarks such as Long Short-Term Memory and Recurrent Neural Networks.

cs.LG↗

arXiv2024

Efficient CNN-LSTM based Parameter Estimation of Levy Driven Stochastic Differential Equations

This study addresses the challenges in parameter estimation of stochastic differential equations driven by non-Gaussian noises, which are critical in understanding dynamic phenomena such as price fluctuations and the spread of infectious diseases. Previous research highlighted the potential of LSTM networks in estimating parameters of alpha stable Levy driven SDEs but faced limitations including high time complexity and constraints of the LSTM chaining property. To mitigate these issues, we introduce the PEnet, a novel CNN-LSTM-based three-stage model that offers an end to end approach with superior accuracy and adaptability to varying data structures, enhanced inference speed for long sequence observations through initial data feature condensation by CNN, and high generalization capability, allowing its application to various complex SDE scenarios. Experiments on synthetic datasets confirm PEnet significant advantage in estimating SDE parameters associated with noise characteristics, establishing it as a competitive method for SDE parameter estimation in the presence of Levy noise.

stat.ML↗

arXiv2022

Estimation of ergodic square-root diffusion under high-frequency sampling

Gaussian quasi-likelihood estimation of the parameter $θ$ in the square-root diffusion process is studied under high frequency sampling. Different from the previous study of Overbeck and Rydén(1998) under low-frequency sampling, high-frequency of data provides very simple form of the asymptotic covariance matrix. Through easy-to-compute preliminary contrast functions, a practical two-stage manner without numerical optimization is formulated in order to conduct not only an asymptotically efficient estimation of the drift parameters, but also high-precision estimator of the diffusion parameter. Simulation experiments are given to illustrate the results.

math.ST↗