We study a nonparametric additive regression model that includes a periodic component, a deterministic time trend, various component functions of stationary covariates and an AR(p) error process that accounts for serial correlation in the regression error.
We propose an estimation procedure for the nonparametric component functions and the parameters of the error process based on smooth backfitting and quasi-maximum likelihood methods.
We establish convergence rates as well as the asymptotic normality of our estimators and conclude by illustrating our estimation procedure by applying it to a sample of climate and ozone data collected on the Antarctic Peninsula.
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