Non-Linearities, Structural Breaks and Fractional Integration in the Analysis of the Ghanaian and the South African CPI Inflation Rates

Keeping a low steady rate of inflation is one of the government’s most important responsibilities. Inflation is an important determinant of economic growth. Consequently, it has been one of the most examined areas in economics, from both theoretical and empirical perspectives. Indeed, economists have shown continued interest in this essential economic variable. The most important question related to inflation is: Does non-linearity exist in inflation? The answer to this question, which has important policy implications, can support or endanger the validity of several important economic models. Hence, a clear understanding of the changing aspects of inflation is crucial to any economy because it is regarded as a significant variable in a number of economic models, whose legitimacy critically relies on whether or not this variable is stationary. In practice, many economic time series models rely on linearity. Nonetheless, it has often been found that simple linear time series models regularly leave certain aspects of economic and financial data inexplicable. This paper proposes a model that combines fractional integration with non-linear deterministic terms based on the Chebyshev polynomials in time for the analysis of CPI inflation rates of Ghana and South Africa in Sub-Saharan Africa. Firstly, we tested for non-linear deterministic terms in the context of fractional integration. The estimates of the differencing parameter, d, were found to be 1.11 and 1.32, respectively for the Ghanaian and the South African inflation rates, but the non-linear trends were found to be statistically insignificant in the two series. A linear model was then investigated and the results indicated that the order of integration for the Ghanaian inflation series was slightly above 1. However, for the case of South Africa, a cyclical I(d) process was found to be more appropriate, with an order of integration below 1, thus showing mean reversion and a cyclical structure of approximately 80 periods (months) per cycle. The implication of these findings could assist in a decision-making process regarding adjusting monetary policy instruments such as inflation targeting (IT) or adopting different monetary policies, to achieve the desired target.