TD_CONVOLVE applies a series representing a digital filter to a time series by convolving the two series. The digital filter can be of any type such as low-pass, band-pass, band-reject, high-pass, and so on.
When you convolve a normal series with a filtered series, the resulting output series contains a combination of the two input series, with some frequency components removed or attenuated due to the filtering operation.
The process involves combining the filtered series over the normal series for each time step, and summing the results. The resulting output series has the same length as the normal series, but the values at each time step are a weighted average of the values in the normal series and the filtered series.
The specific effect of the filtering operation on the output series depends on the characteristics of the filter used and the frequency content of the input series. For example, if a high-pass filter is used to filter the input series, the resulting output series contains mostly high-frequency components, with low-frequency trends or drift removed or attenuated. Similarly, if a low-pass filter is used, the resulting output series contains mostly low-frequency components, with high-frequency noise or fluctuations removed or attenuated.
The convolution of a set of series is useful for various applications, such as signal processing, time series analysis, and machine learning. You can use digital filters to separate time series that have been combined and to restore time series that have become distorted.