Time-series
In this chapter, we are going to briefly introduce the concepts of time-series and stochastic processes. As the topic is very wide, we are only discussing a few fundamental aspects and, at the same time, inviting the reader to refer to a complete book, such as Shumway R. H., Stoffer D. S., Time Series Analysis and Its Applications, Springer, 2017, for all the details.
The main concept of this chapter concerns the structure of a time-series. In this book, we are assuming that we are working with univariate series in the form:
Every value yi depends implicitly on time (that is, yi = y(i)); therefore, the series cannot be shuffled without losing information. If the values yt are completely determined by a law (such as yt = t2), the underlying process is described as deterministic. This is the case with many physical laws, but it's almost useless for us because the future can not be predicted without uncertainty. On the other hand, if every yi is a...