Economic and Financial Cycles in South Africa

Abstract

This study is about cycles. Various cycles are all around us in nature, society and the humans body. However, our interest is in cycles in macroeconomic evolution. Specifically, we focus on business cycles, financial cycles, energy demand cycles and even in climatic change.Some cycles are very regular and therefore easily predictable. The cycles we investigate represent a distinct challenge for research as they are irregular, that is they do not have fixed periods. In many instances studying the cycles is preferred to studying the original as this allows the following:•Data compression/reduction;•Data smoothing, noise reduction, blurring;•Analysis of cycles in many instances is more robust;•Assessing performance of an investor or trader;•Modelling of peaks and troughs;•Comparing cycles (e.g. for synchronisation analysis).In our investigations we used a wide range of techniques – from quite straightforward linear regression (including proposed double-linear or LL-model) to sophisticated hybrid models, combining multivariate regression with artificial neural networks (ANN).The following highlights are mentionable:•Introduction of the concept of axiomatic definition of persistence;•The role of the Hurst exponent in analysis of cycles;•Establishing the link between axiomatic persistence and the Hurst exponent;•New fast method for estimation of Hurst exponent;•Hierarchical optimal dating of cycles in time series;•Hierarchical estimation of time series models, including ANN estimation.For our research we used both real data related to the South African national economy and simulated data. Wolfram Mathematica was used as the principal research tool.