التفاصيل البيبلوغرافية
| العنوان: |
Correlation Matrix Of Equi-Correlated Normal Population: Fluctuation Of The Largest Eigenvalue, Scaling Of The Bulk Eigenvalues, And Stock Market |
| المؤلفون: |
Yohji Akama |
| المصدر: |
World Scientific Publishing Co. Pte. Ltd., International Journal of Theoretical and Applied Finance (IJTAF). 26(02n03):1-27 |
| سنة النشر: |
2023 |
| الوصف: |
Given an N-dimensional sample of size T, form a sample correlation matrix C. Suppose that N and T tend to infinity with T/N converging to a fixed finite constant Q>0. If the population is a factor model, then the eigenvalue distribution of C almost surely converges weakly to MarÄ enko–Pastur distribution such that the index is Q and the scale parameter is the limiting ratio of the specific variance to the ith variable (i→∞). For an N-dimensional normal population with equi-correlation coefficient Ï , which is a one-factor model, for the largest eigenvalue λ of C, we prove that λ/N converges to the equi-correlation coefficient Ï almost surely. These results suggest an important role of an equi-correlated normal population and a factor model in Laloux et al. [(2000) Random matrix theory and financial correlations, International Journal of Theoretical and Applied Finance3 (3), 391–397]: the histogram of the eigenvalue of sample correlation matrix of the returns of stock prices fits the density of MarÄ enko–Pastur distribution of index T/N and scale parameter 1−λ/N. Moreover, we provide the limiting distribution of the largest eigenvalue of a sample covariance matrix of an equi-correlated normal population. We discuss the phase transition as to the decay rate of the equi-correlation coefficient in N. |
| نوع الوثيقة: |
redif-article |
| اللغة: |
English |
| DOI: |
10.1142/S0219024923500061 |
| الإتاحة: |
https://ideas.repec.org/a/wsi/ijtafx/v26y2023i02n03ns0219024923500061.html |
| رقم الأكسشن: |
edsrep.a.wsi.ijtafx.v26y2023i02n03ns0219024923500061 |
| قاعدة البيانات: |
RePEc |
