Spline-backfitted kernel forecasting for functional-coefficient autoregressive models

TL;DR

This paper introduces three forecasting methods for functional coefficient autoregressive models using spline-backfitted local linear smoothing, with theoretical validation and practical application to solar irradiance data.

Contribution

It proposes three novel forecasting methods for FCAR models, including a naive, bootstrap, and multistage approach, with asymptotic efficiency results for the SBLL estimator.

Findings

Naive method performs as well as or better than multistage in simulations.

Asymptotic efficiency of SBLL estimators established.

Naive and multistage methods outperform linear AR models in solar irradiance forecasting.

Abstract

We propose three methods for forecasting a time series modeled using a functional coefficient autoregressive model (FCAR) fit via spline-backfitted local linear (SBLL) smoothing. The three methods are a "naive" plug-in method, a bootstrap method, and a multistage method. We present asymptotic results of the SBLL estimation method for FCAR models and show the estimators are oracally efficient. The three forecasting methods are compared through simulation. We find that the naive method performs just as well as the multistage method and even outperforms it in some situations. We apply the naive and multistage methods to solar irradiance data and compare forecasts based on our method to those of a linear AR model, the model most commonly applied in the solar energy literature.