{"ID":3084836,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-07T03:38:11.424509713Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.05681","arxiv_id":"2606.05681","title":"Local increment inference for time-inhomogeneous drift in Gaussian processes","abstract":"We study statistical inference for deterministic drift structures in Gaussian process models under high-frequency observations.The observed process consists of a centered stationary Gaussian component combined with a broad class of time-inhomogeneous deterministic drifts. To estimate the drift parameter, we introduce a least squares-type contrast based on first-order increments. We establish consistency and asymptotic normality under weak dependence conditions on the Gaussian component. A central feature of the framework is that the rate of convergence of the estimator depends jointly on the local roughness of the Gaussian noise and the long-time information accumulation structure generated by the drift. The theory accommodates a wide range of drift families, including integrable, polynomial-type, and periodic structures. In particular, different drift densities produce qualitatively different statistical regimes, including non-standard rates of convergence and accelerated rates for persistent or growing deterministic structures.","short_abstract":"We study statistical inference for deterministic drift structures in Gaussian process models under high-frequency observations.The observed process consists of a centered stationary Gaussian component combined with a broad class of time-inhomogeneous deterministic drifts. To estimate the drift parameter, we introduce a...","url_abs":"https://arxiv.org/abs/2606.05681","url_pdf":"https://arxiv.org/pdf/2606.05681v1","authors":"[\"Yasutaka Shimizu\"]","published":"2026-06-04T04:03:41Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}