Study on the Interval Time Series Model

• Main Authors: Wei-ChingWang, 王維敬
• Other Authors: Liang-Ching Lin
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/jdsqvj

碩士 === 國立成功大學 === 統計學系 === 105 === In financial economics, a large number of analysis and models were developed based on the daily closing prices, or even at lower frequencies such as weekly or monthly. It may discard some valuable intra-daily information such as the highest and lowest prices. We may regard the highest and lowest prices as an interval valued observations and use some symbolic data methodologies to deal with them. When modelling the interval time series, the most difficulty is to avoid the maximum and minimum values to be crossed with each other. Most of literatures deal this problem by changing the interval time series to be the center and radius of the intervals. Nevertheless, due to the normal assumption for the innovation term, the radius processes may not ensure to be positive. Alternatively, Teles and Brito (2015) proposed the space-time autoregressive (STAR) models. STAR model can exactly ensure the predicted upper values to be larger than lower values but can not in generating simulated data. In this paper, we combine the STAR model with multivariate GARCH to deal with the heteroscedasticity of financial data. Alternatively, we propose a model which directly uses the concept of symbolic data and considers the time varying noise terms simultaneously, namely heteroscedastic auto-inter regressive (HAIR) model. In model comparison, we consider a practically oriented experiment based on 2016 S＆P500 index and provide the comparisons of models we mentioned. In real data analysis, we investigate the in-sample and out-of-sample behavior for each model.