A wavelet-based noise reduction method for time series is proposed. Traditional denoising techniques often adopt a "trial-and-error" approach, which can prove inefficient and may result in suboptimal filtering outcomes. In contrast, our method systematically selects the most suitable wavelet function from a predefined set, along with its associated tuning parameters, to ensure an optimal denoising process. The denoised series produced by this approach maximizes a suitable objective function based on information-theoretic divergence. This is particularly significant in economic time series, which are frequently characterized by non-linear dynamics and erratic patterns, often influenced by measurement errors and various external disturbances. The method's performance is evaluated using time series data derived from the Business Confidence Climate Survey, which is freely and publicly accessible via the World Wide Web through the Italian National Institute of Statistics. The results of our empirical analysis demonstrate the effectiveness of the proposed method in delivering robust filtering capabilities, adeptly distinguishing informative signals from noise, and successfully eliminating uninformative components from the time series. This capability not only enhances the clarity of the data, but also significantly improves the overall reliability of subsequent analyses, such as forecasting.
Livio Fenga (2025) studied this question.