On Parameter Tuning of Butterworth Filters

Tuning order parameters of the Butterworth filters makes it possible to extract certain cyclical components of time series with specified precision. But it comes at the expense of numerical stability: a higher order causes a numerical instability. This paper examines what parameter values should be set for the Butterworth filtering to produce the turning dates of the business cycles consistent with the official reference dates of Japan. The main findings are summarized as follows. First, when the transition bands take frequencies of 12 to 18 months per cycle and 96 to 132 months per cycle, the estimated dates of peaks and troughs are consistent with the officially published reference dates of the business cycles in Japan. The corresponding orders of the filters are 11 and 14 for each transition band. Secondly, the deviations from the reference dates are 2.2 months on average that are comparatively small in the literature. Third, the estimates of the turning points are robust to the chages of the pass bands.Tuning order parameters of the Butterworth filters makes it possible to extract certain cyclical components of time series with specified precision. But it comes at the expense of numerical stability: a higher order causes a numerical instability. This paper examines what parameter values should be set for the Butterworth filtering to produce the turning dates of the business cycles consistent with the official reference dates of Japan. The main findings are summarized as follows. First, when the transition bands take frequencies of 12 to 18 months per cycle and 96 to 132 months per cycle, the estimated dates of peaks and troughs are consistent with the officially published reference dates of the business cycles in Japan. The corresponding orders of the filters are 11 and 14 for each transition band. Secondly, the deviations from the reference dates are 2.2 months on average that are comparatively small in the literature. Third, the estimates of the turning points are robust to the chages of the pass bands.Tuning order parameters of the Butterworth filters makes it possible to extract certain cyclical components of time series with specified precision. But it comes at the expense of numerical stability: a higher order causes a numerical instability. This paper examines what parameter values should be set for the Butterworth filtering to produce the turning dates of the business cycles consistent with the official reference dates of Japan. The main findings are summarized as follows. First, when the transition bands take frequencies of 12 to 18 months per cycle and 96 to 132 months per cycle, the estimated dates of peaks and troughs are consistent with the officially published reference dates of the business cycles in Japan. The corresponding orders of the filters are 11 and 14 for each transition band. Secondly, the deviations from the reference dates are 2.2 months on average that are comparatively small in the literature. Third, the estimates of the turning points are robust to the chages of the pass bands