Optimal Convergence Rates in Non‐Parametric Regression with Fractional Time Series Errors
10 Pages Posted: 23 Dec 2012
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|-α 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: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Recommended Papers
-
Wavelet Multiresolution Analysis of High-Frequency Asian FX Rates, Summer 1997
-
Nonparametric Testing of the High-Frequency Efficiency of the 1997 Asian Foreign Exchange Markets
-
Nonparametric Efficiency Testing of Asian Stock Markets Using Weekly Data
-
Persistence Characteristics of Latin American Financial Markets
By Nyo Nyo A. Kyaw, Cornelis A. Los, ...
-
The International CAPM and a Wavelet-Based Decomposition of Value at Risk
-
The International CAPM and a Wavelet-Based Decomposition of Value at Risk
-
Long Memory Options: Valuation
By Sutthisit Jamdee and Cornelis A. Los
-
Persistence Characteristics of the Chinese Stock Markets
By Cornelis A. Los and Bing Yu
-
Long-Term Dependence Characteristics of European Stock Indices
By Cornelis A. Los and Joanna M. Lipka
Optimal Convergence Rates in Non‐Parametric Regression with Fractional Time Series Errors
This is a Wiley Blackwell - Medium Tier paper. Wiley Blackwell - Medium Tier charges $49.00 .
File name: j-9892.pdf
Size: 685K
If you wish to purchase the right to make copies of this paper for distribution to others, please select the quantity.
