Investigating the Robustness of Filters for Integrated Processes in Business Cycles

Abstract

Time series are frequently filtered to remove unwanted characteristics, such as trends and seasonal components, or to estimate components driven by stochastic cycles from a specific range of periods in a business cycle. A polynomial function of time is the most common deterministic time trend while an integrated process is the most common stochastic trend. The different filters implemented in this paper allow for different orders of deterministic time trends or integrated processes. The robustness of the filters is evaluated by plotting their gain function against the gain function of a simulated ideal filter. Implementing the filters on Nigerian gross domestic products (GDP), the results show that the gain of the Baxter-King (BK) filter deviates markedly from the square-wave gain of the ideal filter. The gain in Christiano–Fitzgerald (CF) filter is closer to the gain of the ideal filter than the BK filter. The gain in Hodrick–Prescott (HP) filter goes to one for those cycles at frequencies above six periods, whereas the other gain functions go to zero. The Butterworth (BW) filter does a reasonable job of filtering out the high-periodicity stochastic cycles but the low- periodicity stochastic cycles is not been completely removed.