TITLE:
Autoregressive Fractionally Integrated Moving Average-Generalized Autoregressive Conditional Heteroskedasticity Model with Level Shift Intervention
AUTHORS:
Lawrence Dhliwayo, Florance Matarise, Charles Chimedza
KEYWORDS:
Fractional Differencing, Long-Memory, Heteroscedasticity, Volatility, Level Shift
JOURNAL NAME:
Open Journal of Statistics,
Vol.10 No.2,
April
29,
2020
ABSTRACT: 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, volatilityand 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.