Filtering And Inference

Many empirical macroeconomic questions rely on filtering non-stationary data to extract a stationary, business-cycle-like component. Common practice is to apply a linear filter with a standard passband, although economically relevant cycles may lie outside this passband. The resulting signal-extraction error likely affects subsequent regression estimates. This paper proposes a Continuous Wavelet Transform-informed filter that uses the CWT scalogram to identify statistically significant passbands in raw, non-stationary data relative to a researcher-specified null model. These passbands are supplied to a flexible Butterworth bandpass filter to extract a denoised, stationary cycle. Simulations show that the method improves signal extraction for periodic cycles and recovers statistically informative variation in stochastic-cycle settings missed by commonly used BK, HP, and Hamilton filters, while performing comparably or better in terms of correlation and RMSE. Applications demonstrate its use for cycle extraction, seasonal adjustment, and frequency-dependent regression analysis.