Time Series Coverage in Engineering (vs. Statistics and Econometrics)

Question

Time Series Analysis is used extensively in many fields such as statistics, mechanical engineering, econometrics, etc. I am trying to get a sense for how the coverage of Time Series Analysis differs across these 3 disciplines. I started this effort by comparing a leading textbook in each field: "Intro to Time Series and Forecasting" Brockwell and Davis in Statistics, "Random Data: Analysis and Measurement Procedures" by Piersol and Bendat in Engineering, and "Time Series Analysis" by Hamilton in Econometrics. People here will certainly be more familiar with the statistics and econometrics angles, but I want to ask: how does the engineering coverage differ, big picture? My sense is that the Engineering book covers everything that is covered in the Statistics and Econometrics books and more, referring to Fast Fourier Transforms, for example. So if I wanted to forecast, say interest rates - something that is not the intended application for the Engineering book, would reading the Engineering book give me everything I need to do that and more? If not, what is it missing?