Satoshi Urasawa

(Deputy Director, Office for Econometric Analysis, Cabinet Office)

Haruki Seitani

(Deputy Director, Office for Econometric Analysis, Cabinet Office)

Statistical filters such as Hodrick-Prescott and Band-pass filters are widely applied in business cycle studies for detrending time series data and measuring their cyclical components, nevertheless theoretical literature has criticized that they may distort the statistical properties of pre-filtered series. In order to factor the theoretical caveats into the practical calculation, this paper provides both Monte-Carlo and Bootstrap simulation-based techniques to construct confidence intervals for the cyclical components obtained by those filters.

Application of the techniques to real output in Japan shows that two-sided 95% confidence intervals for the filtered series range approximately 1% both upper and lower bounds, implying that the output gaps estimated by those filters fluctuating within -1% to +1% are not statistically different from 0%. Interestingly, significant movements in the output gaps coincide with peaks and troughs of business cycles in most cases, although there exists difficulty in assessing output gaps in the latest periods due to expansion of the error bands caused by deteriorations of performance of those filters at the endpoints in sample series.