Non-linear modelling of market cycles in South Africa

Purpose – The purpose of this paper is to expand on the sparse literature on non-linear modelling in South Africa and test for non-linearity of the market cycle on the Johannesburg Stock Exchange, with specific focus on a particular non-linear model – a Smooth Transition Auto-Regressive (STAR) model. Design/methodology/approach – Non-linear estimation methods are used to describe the market cycle, as defined by equity prices, for the period 1998-2010. Findings – In applying the STAR model to daily, weekly and monthly returns data, it was found that the fit of this family of models differs heavily based on the frequency of data used. The daily Logarithmic STAR (LSTAR) model was found to be the best fit relative to other data frequencies. Indeed, the weekly LSTAR model, while still appropriate to use, was less apt at forecasting than its daily counterpart. Monthly return data indicated that a linear AR model was more appropriate than a non-linear one. Practical implications – The results assist in understanding the cyclical nature of emerging markets as well contributing to the understanding of creating a portfolio consisting of international securities. If one can show that equity returns in a particular emerging market follow non-linear behaviour, expanding this hypothesis to other emerging markets enables a minimum variance portfolio to be constructed that is informed by returns changing over time. Originality/value – The findings can be used for further research into share price modelling, portfolio management and perhaps as an avenue into the reasoning behind the formation of market cycles.