# Relations and differences between time-series analysis and statistical signal processing?

I was wondering what relations and differences are between time-series analysis and statistical signal processing?

I found some recommendations of books in time series including some books in statistical signal processing. But I am not sure how these two areas are related and differ?

Thanks and regards!

As a signal is by definition a time series, there is significant overlap between the two.

I would expect a book on time-series analysis to be either a mathematical treatment, or a business/commercial treatment, while a book on statistical signal processing is likely to make heavy use of mathematics, but interested in the problems of signal analysis, classification, noise reduction, and other problems relevant to engineering / applied science.

Statistical signal processing uses the language and techniques of mathematical time-series analysis, but also introduces into the problem domain many concepts and techniques out of electrical engineering: signal to noise, dynamic range, and time/frequency domain transforms.

In my view, time-series analysis is a mathematical field, which then has applications wherever time series tend to crop up. Those fields then develop techniques that are specialised for those problem domains, with a specialised body of knowledge.

As time series arise in business and economics, there is an industry of material on time-series forecasting, trend analysis, etc. Much of this 'commercial' application is not present in the material on statistical signal processing, in part because the nature of the two time series is very different: signals are continuous over both time and measurement variables (e.g. voltage, intensity, etc.) Whereas most business time-series are taken over a discrete time domain (days, weeks, months, quarters, years).

• The contrast of signal processing from electrical engineering and the time series/forecasting does reflect my experience in both fields. Feb 2, 2019 at 23:53

@AKE's answer above is very good but one additional comment I would make is that while there are major overlaps, the differences between signal processing and time-series analysis often arise from the types of data being considered;

Signal processing usually considers the analysis of a 'raw' signal, in that the signal needs to be processed heavily to extract 'features', descriptive parameters that allow the signal to be meaningfully interpreted. For example the origins of statistical signal processing lie in the development of radar technology, the raw radar sensor signal needed to heavily processed and enhanced to allow the operator to make any sense of it and obtain 'useful' data. The extraction of such interpretable parameters can often be the end goal, though often those parameters are in turn used to perform prediction/classification.

In contrast time-series analysis often considers the long-term trends and variations of individual (or groups of) parameters (such financial or economic indicators). Such time-series analysis is often used to predict future behavior. Usually the pre-processing of the time-series parameters (predictors) is of secondary importance to building a predictive or explanatory model.

• Excellent point (+1). An example of 'raw signal': radar/sonar systems often have 4 detectors slightly offset, each continuously returning a voltage v. time signal. The phase difference between these 4 signals is then used to determine the angle from which the source came. This kind of processing is real-time, i.e. has to be done almost at machine speed, and requires analog to digital sampling, one of the cornerstones of signal processing theory (Nyquist theorem, etc.) By contrast, business time-series are almost always part of a data understanding phase, and not hard-real time. Mar 17, 2013 at 17:24