Publication Type
Master Thesis
Version
publishedVersion
Publication Date
2008
Abstract
The existence of second order moment or the finite variance is a commonly used assumption in financial time series analysis. We examine the validation of this condition for main stock index return series by applying the extreme value theory. We compare the performances of the adaptive Hill's estimator and the Smith's estimator for the tail index using Monte Carlo simulations for both i.i.d data and dependent data. The simulation results show that the Hill's estimator with adaptive data-based truncation number performs better in both cases. It has not only smaller bias but also smaller MSE when the true tail index α is not more than 2. Moreover, the Hill's estimator shows precise results for the hypothesis test of infinite variance. Applying the adaptive Hill's estimator to main stock index returns over the world, we find that for most indices, the second moment does exist for daily, weekly and monthly returns. However, an additional test for the existence of the fourth moment shows that generally the fourth moment does not exist, especially for daily returns. And these results don't change when a Gaussian-GARCH effect is removed from the original return series.
Keywords
asymmetric stable Paretian distribution, financial modeling, financial time series, stock price analysis, volatility
Degree Awarded
MSc in Economics
Discipline
Finance | Portfolio and Security Analysis
Supervisor(s)
YU, Jun
Publisher
Singapore Management University
City or Country
Singapore
Citation
YAN, Xian Ning.
Test for Infinite Variance in Stock Returns. (2008).
Available at: https://ink.library.smu.edu.sg/etd_coll/39
Copyright Owner and License
Author
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.