Appendix B
Basics about Stochastic Processes and Time Series
This Appendix Aims to provide a brief survey of some relevant terms and concepts from a basic course about stochastic processes and (continuous-valued) time series analysis. Many more details can be found in introductory textbooks such as those by Box et al. (2015), Brockwell & Davis (2016), Cryer & Chan (2008), Falk et al. (2012), Shumway & Stoffer (2011) and Wei (2006). For Section B.4.2, Lütkepohl (2005) is also recommended as a comprehensive textbook about multivariate time series. For the Markov chains discussed in Section B.2, the book by Seneta (1983) offers a lot of further detail.
B.1 Stochastic Processes: Basic Terms and Concepts
A (discrete-time) stochastic process (or simply process) is a sequence 
of random variables 
defined on a probability space 
and with range 
(the state space of the process), where 
is a discrete and linearly ordered set. For simplicity, we usually choose or . We distinguish between continuous-valued ...
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