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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. Předkládaný článek porovnává tři nejpoužívanější typy filtrů pro analýzu hospodářských cyklů, a to Baxterův-Kingův, Christianův-Fitzgeraldův filtr a filtr typu Hammingovo okno. Empirický přínos publikace je v numerickém ohodnocení aproximace ideálního pásmového filtru na základě zisku, propouštění a zdůraznění frekvenčních složek filtru. Aplikace je provedena na vybrané země EU.

We focus on changes in dynamic correlation during the recent financial crisis. The results show different responses to this symmetric shock in V4 countries. We discuss possible specialization if the dynamic correlation increases only at certain of the frequencies. Especially, in case of the Czech Republic where the variability of dynamic correlation in business cycle frequencies increased in relation to the euro area, whereas decreased in relation to Germany. Consequently, we point out to the limitations of a correlation and concordance index as common indicators of business cycle synchronization in time domain.

The paper provides the methodological background for the Czech Republic business cycle dating process using an alternative approach. This approach is based on the mathematical principle of identification of extremes using estimates of derivations of time trend of the analysed time series, for which the nonparametric Gasser-Muller estimate is used. The presented methodological approach is applied on the real gross domestic product data sets, the total industry (excluding construction), the gross capital formation and the final consumption expenditure. The selected variables are taken from the national accounts system. The obtained results are compared to the widely used naive technique of business cycle dating written by Canova (1998, 1999) or Bonenkamp (2001). The presented new method specifies the identification of turning points in the business cycle dating process.