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