Many economic time series can be decomposed into transitory phenomena, cyclical movements and permanent shifts. Band pass filters such as those proposed by Bax-ter and King (BK) and Christiano and Fitzgerald (CF) can be used to decompose such series without necessitating strong model assumptions on the time series dynamics.

However, both these filters have some known drawbacks. The BK filter can remove trends at the zero frequency effectively, but does not adequately suppress other un-desired low frequency fluctuations. Furthermore, improving the approximation of the frequency response of ideal filters requires sacrificing more observations. The CF fil-ter improves the frequency response approximation, but has deteriorating performance near the end points of the data, and induces phase shift distortions. In this paper we present an approximate band pass filter which overcomes the draw-backs of the previous filters. The filter works by recursively fitting multiple trigonometric functions in the time domain to observed series, and filtering the remaining residual directly in the frequency domain. By only retaining the frequencies in the desired pass band, a band pass filter with desired properties is defined. In particular, the filter does not induce phase shifts and does not require down weighting or removal of any data. We provide two empirical applications of the filter. In the first application we filter Eu-ropean macro-economic output series with business cycle pass bands and make a comparative analysis with the filter output of the BK and CF filters. In the second ap-plication, we perform a bi-orthogonal decomposition using a combination of band pass filtering and principal components analysis to construct a business cycle indicator.

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