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Asset Pricing Models: Specification, Data and Theoretical Foundation Read chapter Read first chapter

2018 | OriginalPaper | Chapter

2. Statistical Inferences with Specification Tests

Author : Jau-Lian Jeng

Published in: Empirical Asset Pricing Models

Publisher: Springer International Publishing

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Abstract

The author discusses the methodologies that are currently applied to empirical asset pricing models on asset returns, including up-to-date coverage on theoretical setting and model specification tests. For instance, factor analysis and (asymptotic) principal component analysis are provided for searching for these pricing cores or kernels of asset returns. Unfortunately, these earlier studies incur the difficulty of observability of these factors and of (economic) interpretation of the principal components. In essence, the application of multi-factor asset pricing models with observed/presumed factors becomes an alternative in the search for the systematic components of asset returns.

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previous chapter Asset Pricing Models: Specification, Data and Theoretical Foundation
next chapter Statistical Inferences with Model Selection Criteria
Footnotes
1
Since x is an n-dimensional vector, the moment condition is applied to each element of the vector. The same assumption holds for the price vector q as well.
 
2
The time subscript is suppressed for simplicity of expression.
 
3
The time sub-index is suppressed for simplicity.
 
4
Later work in Shanken and Zhou (2007) relaxes the assumption of correct specification of factor premiums by introducing a residual or pricing error in the expected returns. However, the analysis is still based on the correct identification of factor structure.
 
5
In fact, this setting is identical to Chamberlain and Rothschild (1983) and Ingersoll (1984) in approximate factor structure.
 
6
Notice that the notation “−∞” does not necessarily mean there are negative infinite observations. It only depicts the possible initial observations of cross-sectional idiosyncratic risk that are distant from the present collections.
 
7
Implicitly, their work assumes that the \(\frac {T}{2}\) is an integer already so that the inter-temporal differences are always feasible.
 
8
This condition is to ensure that asymptotic variance of the cumulative sum of these squared idiosyncratic risks exists and is finite under the null hypothesis.
 
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Metadata
Title
Statistical Inferences with Specification Tests
Author
Jau-Lian Jeng
Copyright Year
2018
Book
Empirical Asset Pricing Models

Print ISBN: 978-3-319-74191-8

Electronic ISBN: 978-3-319-74192-5

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-74192-5_2