Analysis of Symbolic Interval-Valued Variables and Interval Time Series Based on Normal Distribution

Abstract

In this study we establish the fundamental statistical inferences for normality distributed symbolic interval-valued variables They include the mean variance and correlation Further we propose an auto-interval-regressive (AIR) model to characterize the interval time series process The likelihood functions of above models are derived by treating the intervals as the largest and smallest order statistics of a normal distribution To capture the stochastic volatility we combine the AIR model with auto-regressive conditional heteroscedasticity (ARCH) model Simulation studies are performed to demonstrate the accuracy of the estimators In real application we consider two data sets: the air quality monitoring data and S&P 500 index We compare the differences of the loadings of principal component analysis based on daily mean and daily interval-valued data For S&P 500 index the 1-step predictive high and low prices based on AIR-ARCH model dominate the alternatives such as vector autoregressive model and k-nearest neighbors method

Date of Award	2019
Original language	English
Supervisor	Liang-Ching Lin (Supervisor)