Debiased parametric inference for regime-switching jump diffusions with infinite variation jumps

We study high-frequency inference for an ergodic regime-switching jump diffusion with locally stable infinite-variation jumps. The state and the finite-state regime are observed on the same grid. The mesh satisfies $h_n\to 0$, while the horizon satisfies $T_n=n{h}_n\to \mathrm{\infty }$. We estimate structural drift and diffusion parameters in the presence of unknown regime-specific L'evy measures. For a common activity index $1<\beta <8\mathrm{/}5$, we remove two leading jump biases from each regime’s truncated variation. We then combine the diffusion estimator with estimated signed tail means in an adaptive drift contrast. We prove joint asymptotic normality at rates $\sqrt{T_n}$ and $\sqrt{n}$, together with feasible studentization. The growing horizon requires uniform control of the debiasing remainders and random denominators over increasing regime exposures. It also produces an explicit L'evy-measure term in the drift covariance. A fixed-grid median stabilizes the two-step correction without changing its first-order limit. We study finite-sample behavior by simulation and apply the method to 127.5 hours of cattle sensor data. In the application, jaw-activity labels are recorded by a device separate from the sensor that measures the state process.