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has been cited by the following article:

• 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.