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Nonparametric regression with rescaled time series errors
Author(s) -
FigueroaLópez José E.,
Levine Michael
Publication year - 2013
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12017
Subject(s) - mathematics , heteroscedasticity , autoregressive model , asymptotic distribution , estimator , nonparametric regression , nonparametric statistics , statistics , series (stratigraphy) , autocovariance , variance function , mathematical analysis , paleontology , biology , fourier transform
We consider a heteroscedastic nonparametric regression model with an autoregressive error process of finite known order p . The heteroscedasticity is incorporated using a scaling function defined at uniformly spaced design points on an interval [0,1]. We provide an innovative nonparametric estimator of the variance function and establish its consistency and asymptotic normality. We also propose a semiparametric estimator for the vector of autoregressive error process coefficients that is T consistent and asymptotically normal for a sample size T . Explicit asymptotic variance covariance matrix is obtained as well. Finally, the finite sample performance of the proposed method is tested in simulations.