#TITLE_ALTERNATIVE#

• Main Author: TRI HERDIANI (NIM 30104007), ERNA
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/7826
• Institution: Institut Teknologi Bandung

The ability to monitor the stability of a sequence of correlation matrices is very important in application as well as in theoretical studies. We can see in literature that, since the last decade, that problem can be found in a wide spectrum from property business, real estate, asset business, risk management, equity market, stock market, global market and general financial and economic businesses until parallel computation. Theoretically, the theoretical basis already exists since seven decades ago and it continued until last years. In general, the criterion used in this study is the so-called likelihood ratio test (LRT). The most popular and widely used statistics, constructed based on LRT, are Box statistic Kullback statistic, Jennrich statistic, Fisher statistic and Schott statistic. The popularity lies in the easiness of their applications. However, they are not apt for correlation matrices of large dimension. It is caused by the fact that those statistics involve the computation of determinant of correlation matrix and the inversion of a certain matrix. This dissertation introduces a method to monitor the stability of an independent sequence of correlation matrices. The monitoring process will be conducted using Multivariate Statistical Process Control (MSPC) approach where the equality of two correlation matrices is tested repeatedly. For that purpose we propose a statistical test which we call vector variance of standardized variables (VVSV) as a measure of multivariate dispersion when all variables are standardized. In order to use it in inference studies, in this dissertation we derive the asymptotic distribution of sample VVSV in normality assumption. Furthermore, we show that, in general, the power of VVSV statistic is better than the most popular statistic, i.e., Jennrich statistic. Another advantage of VVSV statistic is that its computational complexity is lower than Jennrich statistic. If the latter involves the inversion of two matrices, the former is only the sum of square of all elements of correlation matrices.