Abstract
SUMMARY We estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model. Unknown parameters are estimated by either maximum likelihood, cross-validation or generalized cross-validation. By expressing the problem in state space form we obtain 0(n) algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross-validation functions. The finite sample properties of the function estimates are evaluated by an extensive simulation study and examples are given.
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