Functional regression models for South African economic indicators: a growth curve perspective

摘要

In this paper, we compare three functional regression models from a growth curve perspective to predict the relationship between two economic variables, specifically we compare a functional concurrent model, a functional historical model and a functional autoregressive model (FAR). The dependent and the independent variables are cumulated over the annual time window for the growth curve analyses. These models are used to predict exports (real) for the South African economy in terms of electricity demand. The data analysed consist of 33 years of exports (in ZAR million) at annual quarterly frequency, and electricity demand (in GwH) at monthly totals. Exploratory analysis included phase-plane plots for the two series. For the prediction exercise, the baseline concurrent model was evaluated against the other two models, and their performance compared using the root-mean-square error (RSME) measure, the relative performance in terms of the ratio of the RMSEs, and a Kolmogorov-Smirnov based hypothesis test to compare the distributions of the RMSEs of the models. Our results show that from the growth curve perspective, for the prediction of exports in terms of electricity for the SA economy, the FAR model of lag(l) outperforms both the concurrent model and the historical model by far.