Autoregressive Fractionally Integrated Moving Average-Generalized Autoregressive Conditional Heteroskedasticity Model with Level Shift Intervention

• 作者: Charles Chimedza Florance Matarise Lawrence Dhliwayo
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: Fractional Differencing LONG-MEMORY HETEROSCEDASTICITY VOLATILITY Level SHIFT
• 年，卷（期）: 2020,（2）
• 页码范围: 341-362
• 页数: 22页
• 分类号: O17

摘要

In this paper, we introduce the class of autoregressive fractionally integrated moving average-generalized autoregressive conditional heteroskedasticity?(ARFIMA-GARCH) models with level shift type intervention that are capable of capturing three key features of time series: long range dependence, volatility?and level shift. The main concern is on detection of mean and volatility level shift in a fractionally integrated time series with volatility. We will denote such a time series as level shift autoregressive fractionally integrated moving average (LS-ARFIMA) and level shift generalized autoregressive conditional heteroskedasticity (LS-GARCH). Test statistics that are useful to examine if mean and volatility level shifts are present in an autoregressive fractionally integrated moving average-generalized autoregressive conditional heteroskedasticity (ARFIMA-GARCH) model are derived. Quasi maximum likelihood estimation of the model is also considered.