# 9. Principal Component Analysis and Factor Models

Published Online: 2 AUG 2010

DOI: 10.1002/9780470644560.ch9

Copyright © 2010 John Wiley & Sons, Inc.

Book Title

## Analysis of Financial Time Series, Third Edition, Third Edition

Additional Information

#### How to Cite

Tsay, R. S. (2010) Principal Component Analysis and Factor Models, in Analysis of Financial Time Series, Third Edition, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470644560.ch9

#### Publication History

- Published Online: 2 AUG 2010
- Published Print: 13 AUG 2010

#### Book Series:

#### Book Series Editors:

- Walter A. Shewhart and
- Samuel S. Wilks

#### ISBN Information

Print ISBN: 9780470414354

Online ISBN: 9780470644560

- Summary
- Chapter
- References

### Keywords:

- asymptotic principal component analysis;
- fundamental factor models;
- macroeconometric factor models;
- principal component analysis (PCA);
- statistical factor analysis

### Summary

To simplify the task of modeling multiple returns, this chapter discusses some dimension reduction methods to search for the underlying structure of the assets. *Principal component analysis* (PCA) is perhaps the most commonly used statistical method in dimension reduction, and the discussion starts with this method. The chapter introduces some useful factor models and demonstrates their applications in finance. It explains a general factor model for asset returns, and discusses macroeconomic factor models with some simple examples. The fundamental factor model and its applications are given in the chapter and it examines principal component analysis that serves as the basic method for statistical factor analysis. The PCA can also be used to reduce the dimension in multivariate analysis. The chapter discusses the orthogonal factor models, including factor rotation and its estimation and provides several examples. Finally, it ends with asymptotic principal component analysis.

#### Controlled Vocabulary Terms

principal components analysis