Optimal Convergence Rates in Non‐Parametric Regression with Fractional Time Series Errors

10 Pages Posted: 23 Dec 2012

See all articles by Yuanhua Feng

Yuanhua Feng

University of Paderborn

Jan Beran

University of Konstanz

Date Written: January 2013

Abstract

Consider the estimation of g(v), the νth derivative of the mean function, in a fixed‐design non‐parametric regression model with stationary time series errors ξi. We assume that g ∈ Ck, ξi are obtained by applying an invertible linear filter to iid innovations, and the spectral density of ξi has the form f(λ) ~ cf|λ| as λ→0 with constants cf >0 and α ∈ (−1,1). Under regularity conditions, the optimal convergence rate of ^g(v) is shown to be n-rv with rv=(1−α)(k−ν)/(2k+1−α). This rate is achieved by local polynomial fitting. Moreover, in spite of including long memory and antipersistence, the required conditions on the innovation distribution turn out to be the same as in non‐parametric regression with iid errors.

Keywords: Optimal rate of convergence, non‐parametric regression, long memory, antipersistence

Suggested Citation

Feng, Yuanhua and Beran, Jan, Optimal Convergence Rates in Non‐Parametric Regression with Fractional Time Series Errors (January 2013). Journal of Time Series Analysis, Vol. 34, Issue 1, pp. 30-39, 2013, Available at SSRN: https://ssrn.com/abstract=2193199 or http://dx.doi.org/10.1111/j.1467-9892.2012.00811.x

Yuanhua Feng (Contact Author)

University of Paderborn ( email )

Warburger Str. 100
Paderborn, D-33098
Germany

Jan Beran

University of Konstanz

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