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Fourier, Hodrick Prescott Filter, Baxter-King Filter, Empirical Mode Decomposition
A Fourier transform analysis is proposed to determine the duration of the South African business cycle, measured using log changes in nominal gross domestic product (GDP). The most prominent cycle (two smaller, but significant, cycles are also present in the time series) is found to be 7.1 years, confirmed using Empirical Mode Decomposition. The three dominant cycles are used to estimate a 3.5 year forecast of log monthly nominal GDP and these forecasts compared to observed (historical) data. Promising forecast potential is found with this significantly-reduced number of cycle components than embedded in the original series. Fourier analysis is effective in estimating the length of the business cycle, as well as in determining the current position (phase) of the economy in the business cycle.