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Additive nonparametric regression with autocorrelated errors
Author(s) -
Smith Michael,
Wong ChiMing,
Kohn Robert
Publication year - 1998
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00127
Subject(s) - autoregressive model , autocorrelation , markov chain monte carlo , nonparametric regression , mathematics , nonparametric statistics , statistics , markov chain , model selection , bayesian probability , econometrics , computer science
A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially non‐linear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach also allows the selection of a suitable transformation of the dependent variable. All aspects of the model are estimated simultaneously by using the Markov chain Monte Carlo method. It is shown empirically that the approach proposed works well on several simulated and real examples.