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

TL;DR

This paper introduces a flexible semi-parametric regression approach combining penalised splines and autoregressive errors to improve forecasting of ultrafine particle concentrations, capturing trends and autocorrelation in time series data.

Contribution

It presents a novel method integrating spline-based regression with autoregressive error modeling for better time series forecasting.

Findings

Effective in simulated data

Successfully applied to real-world ultrafine particle data

Provides more realistic forecasts by modeling residual autocorrelation

Abstract

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.