Here it says
In mathematics, deconvolution is an algorithm-based process used to enhance signals from recorded data. Where the recorded data can be modeled as a pure signal that is distorted by a filter (a process known as convolution), deconvolution can be used to restore the original signal.1 The concept of deconvolution is widely used in the techniques of signal processing and image processing.
The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book Extrapolation, Interpolation, and Smoothing of Stationary Time Series (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of weather forecasting and economics.
How exactly is deconvolution applied on econometric time series? what are good present-day examples, or from those "early attempts", that really demonstrate the value that deconvolution brings to economics, as said above?