Additive Nonparametric Regression with Autocorrelated Errors

A Bayesian approach is presented for estimating nonparametrically an additive regression model with autocorrelated errors. Each of the potentially nonlinear components is modeled as a regression spline using many knots, while the errors are modeled by a high order stationary autoregressive process parameterized in terms of its partial autocorrelations. Significant knots and partial autocorrelations are selected using variable selection. All aspects of the model are estimated simultaneously using Markov chain Monte Carlo. It is shown empirically that the proposed approach works well on a number of simulated examples. 1 Introduction When a regression model is fitted to time series data the errors are often likely to be autocorrelated, such as in the problems tackled by Engle, Granger, Rice and Weiss (1986) and Harvey and Koopman (1993). Few approaches are currently available for estimating a regression model nonparametrically when the errors are autocorrelated, despite the fact that fai..