Model Identification and Data Analysis

Today, a deluge of information is available in a variety of formats. Industrial plants are equipped with distributed sensors and smart metering; huge data repositories are preserved in public and private institutions; computer net- works spread bits in any corner of the world at unexpected speed. No doubt, we live in the age of data. ᘐis new scenario in the history of humanity has made it possible to use new paradigms to deal with old problems and, at the same time, has led to challeng- ing questions never addressed before. To reveal the information content hidden in observations, models have to be constructed and analyzed. ᘐe purpose of this book is to present the first principles of model construc- tion from data in a simple form, so as to make the treatment accessible to a wide audience. As R.E. Kalman (1930–2016) used to say “Let the data speak,” this is precisely our objective. Our path is organized as follows. We begin by studying signals with stationary characteristics (Chapter 1). After a brief presentation of the basic notions of random variable and random vector, we come to the definition of white noise, a peculiar process through which one can construct a fairly general family of models suitable for describ- ing random signals. ᘐen we move on to the realm of frequency domain by introducing a spectral characterization of data. ᘐe final goal of this chapter is to identify a wise representation of a stationary process suitable for developing prediction theory.