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SEMIPARAMETRIC TIME SERIES REGRESSION
Author(s) -
Truong Young K.,
Stone Charles J.
Publication year - 1994
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/j.1467-9892.1994.tb00202.x
Subject(s) - mathematics , autoregressive model , bivariate analysis , series (stratigraphy) , realization (probability) , semiparametric regression , nonparametric regression , regression function , nonparametric statistics , moving average model , function (biology) , semiparametric model , parametric statistics , regression , stationary process , statistics , time series , component (thermodynamics) , regression analysis , autoregressive integrated moving average , paleontology , physics , evolutionary biology , biology , thermodynamics
Abstract. Let ( X i , Y i ), i = 0, pL 1,… denote a bivariate stationary time series with X i being R d ‐valued and Y i being real‐valued. We consider the regression model Y i =θ( X i ) + Z i , where θ(·) is an unknown function and Z i is an autoregressive process. Given a realization of length n , we examine the problem of estimating the nonparametric function θ(·) and the parametric component Z i . Under appropriate regularity conditions, it is shown that both components can be optimally estimated.