# 8. Nonstationarity

Published Online: 28 JAN 2011

DOI: 10.1002/9781118032466.ch8

Copyright © 2010 John Wiley & Sons, Inc. All rights reserved

Book Title

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

Additional Information

#### How to Cite

Chan, N. H. (2010) Nonstationarity, in Time Series: Applications to Finance with R and S-Plus, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032466.ch8

#### Publication History

- Published Online: 28 JAN 2011
- Published Print: 13 SEP 2010

#### Book Series:

#### ISBN Information

Print ISBN: 9780470583623

Online ISBN: 9781118032466

- Summary
- Chapter

### Keywords:

- Brownian motion;
- mean;
- nonstationary;
- random walk model;
- time series;
- unit root tests;
- variance

### Summary

A nonstationary time series may exhibit a systematic change in mean, variance, or both. This chapter develops some intuitive ideas regarding dealing with nonstationary time series. Since the definition of nonstationarity varies, the chapter focuses on a special form of nonstationarity that occurs most often in econometrics and financial time series (i.e., nonstationarity in the mean level of the series). It starts with a brief discussion of the transformation of nonstationary time series with nonconstant variances. The chapter also presents the nonstationarity time series in the mean level. Then, it discusses random walk model under regression coefficient H, and statistical tests for this kind of model are collectively known in the time series and econometric literature as random walk or unit root tests. Finally, the chapter explains how to use a discretized version of central limit theorem to simulate the sample path of Brownian motion.

#### Controlled Vocabulary Terms

mean; nonstationarity; random walk models; unit root principle; variance