2. Probability Models

  1. Ngai Hang Chan

Published Online: 28 JAN 2011

DOI: 10.1002/9781118032466.ch2

Time Series: Applications to Finance with R and S-Plus, Second Edition

Time Series: Applications to Finance with R and S-Plus, Second Edition

How to Cite

Chan, N. H. (2010) Probability Models, in Time Series: Applications to Finance with R and S-Plus, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032466.ch2

Author Information

  1. The Chinese University of Hong Kong, Department of Statistics, Shatin, Hong Kong

Publication History

  1. Published Online: 28 JAN 2011
  2. Published Print: 13 SEP 2010

ISBN Information

Print ISBN: 9780470583623

Online ISBN: 9781118032466

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Keywords:

  • autocorrelation function (ACF);
  • finite-dimensional distributions;
  • Kolmogorov's consistency theorem;
  • probability theories;
  • stochastic processes;
  • time series modeling

Summary

To gain a better understanding of the microscopic component {Nt}, basic probability theories of stochastic processes have to be introduced. This chapter presents the basic probability theories of stochastic processes. Although one may argue that it is sufficient for a practitioner to analyze a time series without worrying about the technical details, a balanced learning between theory and practice would be much more beneficial. It is vital to acquire some basic understanding of the theoretical underpinnings of the subject so that when new ideas emerge, we can continue learning on our own. Kolmogorov's consistency theorem ensures the existence of a stochastic process through specification of the collection of all finite-dimensional distributions. The chapter provides examples which suggest that we can “identify” a time series through inspection of its autocorrelation function (ACF).

Controlled Vocabulary Terms

autocorrelation function; Kolmogorov theorem; probability density function; stochastic process; time series