Modelling Volatility and Level Shift in Fractionally Integrated Processes

We introduce the class of ARFIMA-GARCH (autoregressive fractionally integrated moving average-generalized autoregressive conditional heteroskedasticity) models with level shift type intervention in this paper. These models are capable of capturing three key features of time series: long range dependence, volatility, and level shift. In a fractionally integrated time series with volatility, the key challenge is detecting mean and volatility level shifts. Level shift autoregressive fractionally integrated moving average (LS-ARFIMA) and level shift generalised autoregressive conditional heteroskedasticity will be used to describe such time series (LS-GARCH). In an autoregressive fractionally integrated moving average-generalized autoregressive conditional heteroskedasticity (ARFIMA-GARCH) model, test statistics are obtained that can be used to see if mean and volatility level shifts are present. The model is also estimated using quasi-maximum likelihood estimation.

Author(S) Details

Lawrence Dhliwayo
Department of Statistics, University of Zimbabwe, Harare, Zimbabwe.

Florance Matarise
School of Statistics and Actuarial Science, University of Witwatersrand, Johannesburg, South Africa.

Charles Chimedza
School of Statistics and Actuarial Science, University of Witwatersrand, Johannesburg, South Africa.

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