Author(s)

Lawrence Dhliwayo¹, Florance Matarise¹, Charles Chimedza²

¹Department of Statistics, University of Zimbabwe, Harare, Zimbabwe.
²School of Statistics and Actuarial Science, University of Witwatersrand, Johannesburg, South Africa.

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.

Fractional Differencing, Long-Memory, Heteroscedasticity, Volatility, Level Shift

Dhliwayo, L. , Matarise, F. and Chimedza, C. (2020) Autoregressive Fractionally Integrated Moving Average-Generalized Autoregressive Conditional Heteroskedasticity Model with Level Shift Intervention. Open Journal of Statistics, 10, 341-362. doi: 10.4236/ojs.2020.102023.