Band-pass filters and business cycle analysis: Highfrequency and medium-term deviation cycles in South Africa and what they measure

Many analysts use band-pass filters to remove so-called permanent components from output and then study the remainder, which is then termed the “business cycle”. Building on the critique of these deviation cycles by Harding and Pagan and on the recent work on the mediumterm persistence of business cycles by Comin and Gertler, we study the extent of information loss accompanying this practice. Specifically, we compare the properties of deviation cycles obtained when allowing and disallowing medium-run information to be included with the permanent component and show the dramatic differences in stylized facts. The paper then considers the economic context of high-frequency and medium-term deviation cycles. The results suggest that the high-frequency deviation cycle is not an appropriate measure of demand shocks, which are equally approximated by the medium-term deviation cycle — even though the two cycles differ significantly in terms of persistence, volatility and co-movement with cycles in the US, UK, Europe and Australia. The medium-term deviation cycle appears to capture the cumulated demand and supply shocks to the economy, which is relevant for medium-run analysis but is not useful for business cycle research. The study focuses on four sample periods, one longer and one shorter sample period as well as one including and one excluding the recent financial crisis period, and the results therefore also shed light on whether and how the financial crisis and structural change in South Africa may alter conclusions.