Speaker：Prof. Liang-Ching Lin (Department of Statistics, NCKU)
Topic：Symbolic Interval-valued Data Analysis with Applications to Control Chart and Portfolio Selection
Speaker：Prof. Liang-Ching Lin (Department of Statistics, NCKU)
Date Time：Fri. Sep 6, 2024, 10:40-11:30
Place： 4F-427, Assembly Building I
Online Seminars- Google Meet
Abstract
In this talk, I will briefly introduce my recent developments in symbolic interval-value data analysis. We characterize the symbolic interval-valued data as the order statistics from normal distributions. An approximate expectation formula of order statistics from the normal distribution is used in the univariate case to estimate the mean and variance via the method of moments. In addition, we consider the bivariate case wherein we use the maximum likelihood estimator calculated from the likelihood function derived under a bivariate copula. Then, we develop the symbolic principal component analysis and establish the procedures for the interval-valued statistical control chart based on the univariate and bivariate interval-valued variables. Besides, in application to Merton’s portfolio selection, we propose an interval-valued time series model, including the daily maximum, minimum, and closing prices, and then apply the proposed model to estimate the parameters. The likelihood function and the corresponding maximum likelihood estimates are obtained by stochastic differential equation and the Girsanov theorem. In addition, we use the LightGBM to predict the transaction directions and include not only the prices as convention but also many statistics to be the features. In real data analyses, we consider the photochemical pollutants and the portfolio selection. In the former case, we monitor the photochemical pollutants by using the interval-valued statistical control charts based on the symbolic principal component scores. The results particularly show the superiority over the conventional method that uses the averages to identify the date on which the abnormal maximum occurred. In the latter case, we demonstrate the usefulness of combining the methods above by showing the portfolio profits of selecting 10 stocks in 2018 and 2019. The results particularly show the superiority of the proposed strategy over the conventional method: the profits are almost positive and have around 32% to 72% annually.
Keywords: interval-valued time-series models, LightGBM, order statistics, quality control, symbolic data analysis