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

• Published date: 01 June 2019
• Author: Siphumlile Mangisa,Gary Sharp,Surajit Ray,Sonali Das
• DOI: http://doi.org/10.1111/opec.12148
• Date: 01 June 2019

Functional regression models for South

African economic indicators: a growth curve

perspective

Siphumlile Mangisa*, Sonali Das*,**, Surajit Ray*** and Gary Sharp*

*Department of Statistics, Nelson Mandela University, Port Elizabeth, South Africa. Emails:

Siphumlile.Mangisa@mandela.ac.za; Gary.Sharp@mandela.ac.za

**Advanced Mathematical Modelling, Modelling and Digital Science, Council for Scientific and Industrial

Research, PO Box 395, Pretoria 0001, South Africa. Emails: sonali.the@gmail.com, sdas@csir.co.za

***School of Mathematics and Statistics, University of Glasgow, Glasgow, UK. Email:

Surajit.Ray@glasgow.ac.uk

Abstract

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(1) outperforms both the concurrent model and the historical

model by far.

1. Introduction

In this paper, three novel competing functional growth curve regression models are

explored, namely, the functional concurrent model, the functional historical model and

the functional autoregressive model to investigate the relationship between electricity

demand and the real exports of goods and services index (simply referred to as exports,

hereafter). Both electricity demand and exports are vital indicators of economic growth,

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and it is useful to ascertain how the changes in one variable, in our case electricity

demand, affects the changes in the other variable, in our case exports. We use novel

features in Functional Data Analysis (FDA) methods to compare the within year

seasonal changes and fluctuations in the two series, and to forecast the dependent

variable. In FDA, data are modelled as functions rather than as data points. The

researchers in this paper do not assume causality or prove causality between the two

variables subjected to investigation here, but are interested in fully evaluating the

relationship between exports and electricity demand for the period under study. It is our

view that the standard regression methods do not focus on the differences between inter-

annual seasonal variations. Also, it has been argued that seasonal variations are an

integral component of the continuous time dynamics represented in certain data sets, and

that seasonality should not be treated as a ‘nuisance component’that must be eliminated,

as is the common assumption in the analysis of economic time series in which the

calculation of seasonally adjusted data is an important aspect (Ramsay and Ramsey,

2002). It is our hypothesis too, that these inter-annual seasonal variations are important

and should not be ignored.

South Africa’s electricity demand and exports have been on an increasing trend since

the early 1990s (see Fig.1). This is to be expected as South Africa experienced huge

political and economic changes during 1990–1994, with the South African economy

being opened to the rest of the world post 1994. The economy is maintained and driven

by energy, which in South Africa continues to be primarily electricity. So, electricity

demand is vital to economic growth in South Africa. Indeed, it has been shown by

Ferguson et al. (2000) in a study of over one hundred countries constituting over 99 per

cent of the global economy that electricity consumption is correlated with wealth

creation. Ferguson et al. (2000) do not prove causality, but do ‘show that, in the

technological world of the late 20th century, economic development occurred ‘hand in

hand’with electricity consumption and, in particular, with an increase in the proportion

of energy used in the form of electricity’. It is our view that the same can be said of

exports as they bring in much-needed foreign revenue and directly contribute to job

creation and economic growth in South Africa.

1.1. Literature review of the problem

In analysing the relationship between any two economic variables, time series analysis

methods are very popular and the theoretical literature is well established. To our

knowledge, literature investigating relationships between electricity demand and

economic growth, and between exports and economic growth are limited. Exports are

a major contributor to the Gross Domestic Product (GDP), an acceptable measure of

economic growth (according to World Bank data, exports accounted for just less than 30

per cent of South Africa’s GDP in 2016). Also, most literature is aimed at more than just

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