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Observational time series data often exhibit both cyclic temporal trends andautocorrelation and may also depend on covariates. As such, there is a need forflexible regression models that are able to capture these trends and model anyresidual autocorrelation simultaneously. Modelling the autocorrelation in theresiduals leads to more realistic forecasts than an assumption of independence.In this paper we propose a method which combines spline-based semi-parametricregression modelling with the modelling of auto-regressive errors.  The method is applied to a simulated data set in order to show its efficacyand to ultrafine particle number concentration in Helsinki, Finland, to showits use in real world problems.

Bayesian semi-parametric forecasting of ultrafine particle number concentration with penalised splines and autoregressive errors