Essentials of Time Series for Financial Applications

Appendix A

Mathematical and Statistical Appendix

A Fundamental Statistical Definitions

A.1 Random Variables

Every bit of data that we may collect to implement one of the empirical analyses described in this textbook is seen in statistics and econometrics, as a realization of a random variable, which is a function that may assume one among different values as a result of a random experiment or phenomenon, according to some structure, a probability law. Consider for instance the daily closing return on a stock. In statistics, analysts consider the observed return as a realization of a corresponding random variable, meaning that, before the closure of the market, there exist many possible values for the stock return and, when the market closes, we ...