Thursday, November 16, 2021. Prof. Liang-Ching Lin(Department of Statistics, National Cheng Kung University)
Thursday, November 16, 2021
Venue: Mathematics Building Room 527
Prof. Liang-Ching Lin
(Department of Statistics, National Cheng Kung University)
Symbolic Interval-Valued Time Series Models — GHVAIRMA Models
In recent years, the modern data architecture is recorded in short time intervals while it still contains rich resources of information. Such kind of data may encounter several problems such as missing data, repeated observations, and recording on the non-equidistant time points. To resolve these, researchers have considered reorganizing the data into the form of an interval-valued data consisting of daily or weekly maximum and minimum values as it can preserve more information than the merely aggregated daily or weekly mean data. To characterize such data, we propose an auto-interval-regressive moving averaging (AIRMA) model by using the order statistics from normal distributions. Furthermore, to better capture the heteroscedasticity in volatility, we design a generalized heteroscedastic volatility (GHV) model, which can be combined with the AIRMA model to be a GHVAIRMA model. We derive the likelihood functions of the aforementioned models to obtain the maximum likelihood estimators. Monte Carlo simulations are then conducted to evaluate our methods of estimation and confirm their validity. Real data examples from the S&P 500 Index and PM2.5 levels are used to demonstrate our method.
Keywords: auto-interval-regressive moving averaging model, heteroscedastic volatility, interval-valued data, order statistics, symbolic data analysis.