{"ID":2877690,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.19949","arxiv_id":"2508.19949","title":"Estimating non-linear functionals of trawl processes","abstract":"Trawl processes are a family of continuous-time, infinitely divisible, stationary processes whose correlation structure is entirely characterized by their so-called trawl function. This paper investigates the problem of estimating non-linear functionals of a trawl function under in-fill and long-span sampling schemes. Specifically, building on the work of \\cite{SauriVeraart23}, we introduce non-parametric estimators for functionals of the type $Ψ_{t}(g)=\\int_{0}^{t}g(a(s))\\mathrm{d}s$ and $ Λ_t(g)=\\int_{t}^{\\infty}g(a(s))\\mathrm{d}s$, where $a$ represents the trawl function of interest and $g$ a non-linear test function. We show that our estimator for $Ψ_{t}(g)$ is consistent and asymptotically Gaussian regardless of the memory of the process. We further demonstrate that the same phenomenon occurs for the estimation of $Λ_t(g)$ as long as $g(x)= \\mathrm{O} (\\lvert x\\rvert^p)$, as $x\\to0$, for some $p\u003e3$. Additionally, we illustrate how our results can be used to construct a test statistic robust to memory effects for the presence of $T$-dependent.","short_abstract":"Trawl processes are a family of continuous-time, infinitely divisible, stationary processes whose correlation structure is entirely characterized by their so-called trawl function. This paper investigates the problem of estimating non-linear functionals of a trawl function under in-fill and long-span sampling schemes....","url_abs":"https://arxiv.org/abs/2508.19949","url_pdf":"https://arxiv.org/pdf/2508.19949v3","authors":"[\"Orimar Sauri\"]","published":"2025-08-27T15:03:55Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}