We consider nonparametric smoothing for time series which are clearly non-Gaussian and which are subject to an autoregressive random component. This generalizes methods for smoothing Gaussian series with autoregressive errors, but in the non-Gaussian case the autoregressive structure is not always additive. The problem can be formulated in a general way to include many common non-Gaussian autoregressive models. The amount of smoothing can be chosen by penalized likelihood methods, and we give simulations and parametric bootstrap methods for studying and empirically estimating the penalty …