Empirical evidence of ideal filter approximation: pheriperal and selected EU countries application

Abstract

We compare three filters commonly used for business cycle analysis: the Baxter-King, the Christiano-Fitzgerald and the Hamming window filter. Empirical contribution of the paper is numerical evaluation of the approximation of the ideal band-pass filters in the discussion of the filters theoretical properties (gain and attenuation within the business cycle frequencies, as well as the leakage in the remaining frequencies). We consider the truncation factor for the Baxter-King filter and the sample size for the latter two. We show that the leakage and attenuation of the Christiano-Fitzgerald and the Hamming window filter perform similarly across the range of chosen sample sizes and better than the Baxter-King filter. Moreover, we apply the filters to data of selected EU countries and point out differences in their estimation of growth business cycles. Our findings indicate that Christiano-Fitzgerald filter and the Hamming window both are appropriate for the identification of a business cycle. The Hamming window filter introduces smaller attenuation near the edges but in case of small samples its approximation of ideal filter is very rough.We compare three filters commonly used for business cycle analysis: the Baxter-King, the Christiano-Fitzgerald and the Hamming window filter. Empirical contribution of the paper is numerical evaluation of the approximation of the ideal band-pass filters in the discussion of the filters theoretical properties (gain and attenuation within the business cycle frequencies, as well as the leakage in the remaining frequencies). We consider the truncation factor for the Baxter-King filter and the sample size for the latter two. We show that the leakage and attenuation of the Christiano-Fitzgerald and the Hamming window filter perform similarly across the range of chosen sample sizes and better than the Baxter-King filter. Moreover, we apply the filters to data of selected EU countries and point out differences in their estimation of growth business cycles. Our findings indicate that Christiano-Fitzgerald filter and the Hamming window both are appropriate for the identification of a business cycle. The Hamming window filter introduces smaller attenuation near the edges but in case of small samples its approximation of ideal filter is very rough.