Abstract
Extending the ideas of [7], this paper aims at providing a kernel based non-parametric estimation of a new class of time varying AR(1) processes (Xt), with local stationarity and periodic features (with a known period T), inducing the definition Xt = at(t/nT)X t−1 + ξt for t ∈ N and with a t+T ≡ at. Central limit theorems are established for kernel estima-tors as(u) reaching classical minimax rates and only requiring low order moment conditions of the white noise (ξt)t up to the second order.
Highlights
Since the seminal paper [5], the local-stationarity property provides new models and approaches for introducing non-stationarity in times series
Such models has been studied in many papers, especially concerning the parametric, semi-parametric or non-parametric estimations of functions αj, βk or γj, or other functions depending on these functions; see, for instance references [6], [8], [7], or [3], [11]
For the case ρ = 2 in case the derivatives of as are regular around the point u, the optimal window width may be used and the central limit theorem again holds with a non-centred Gaussian limit
Summary
Since the seminal paper [5], the local-stationarity property provides new models and approaches for introducing non-stationarity in times series. Where T ∈ N∗ is a fixed and known integer number, and (ξt) a white noise The choice of such extension of the tvAR(1) processes is relative to modelling considerations: for instance, in the climatic framework, [4] considered models of air temperatures where the function of interest writes as the product of a periodic sequence by a locally varying function. Bardet and Doukhan/Non-parametric estimation of periodic time varying AR(1) processes where (Zt) is a sequence of i.i.d. random vectors modelling for instance exogenous inputs. This more tough case is deferred to forthcoming papers. Asymptotic normality of a non-parametric estimator for periodic tvAR(1) processes
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
