Extracting business cycles with three filters: A comparative study and application in the case of China

This paper aims to evaluate the performances of the wavelet, Hodrick–Prescott (HP), and Baxter–King (BK) filters in extracting cyclical information and to use an appropriate method to analyze China's business cycles. First, we use a second‐order autoregression (AR (2)) and random walk, based on Monte Carlo simulation experiments, to generate the data‐generating processes (DGPs) with different frequency characteristics. Second, the HP, BK, and wavelet filters are applied to extract the cyclical components of the respective DGPs. Third, the filtering abilities of the three methods are statistically compared. The results show the following: (1) Under the condition that the DGP is low frequency (long cycle) and trend dominated, the filtering performance of the three methods will remain unsatisfactory. (2) If the DGP is high frequency (short cycle), all three methods can serve as effective methods regardless of whether they are trend dominated or cycle dominated. However, it can be seen that the BK and wavelet filters present better performance than the HP filter. (3) In other cases, better filtering performances can be observed in the wavelet. Finally, the three methods are applied to estimate China's business cycles. In conclusion, this paper argues that the wavelet can effectively replace HP and BK filters to extract cyclical components.