Modelling Seasonal Volatility and Level Shift in Fractionally Integrated Processes| Chapter 9 | Research Highlights in Mathematics and Computer Science Vol. 2

 This member introduces a class of migratory fractionally joined autoregressive moving average-statement conditional heteroscedasticity (SARFIMAGARCH) models, accompanying level shift type intervention that are worthy capturing together four key features momentary series: seasonality, long range reliance, volatility and level shift. The main focus act modelling migratory level shift (SLS) in fractionally joined and volatile processes. A normal extension of the seasonal level shift discovery test of the mean for a realization momentary series fulfilling SLS-SARFIMA and SLS-GARCH models was derived. Test enumerations that are useful to test if seasonal level shift in an SARFIMA-GARCH model is statistically believable were introduced. Estimation of SLS-SARFIMA and SLS-GARCH limits are also likely.

Author(s) Details:

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

Florance Matarise,
Department of Statistics, University of Zimbabwe, Harare, Zimbabwe.

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

Please see the link here: https://stm.bookpi.org/RHMCS-V2/article/view/8659

Modelling Volatility and Level Shift in Fractionally Integrated Processes | Chapter 11 | Novel Research Aspects in Mathematical and Computer Science Vol. 1

 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.

View Book:- https://stm.bookpi.org/NRAMCS-V1/article/view/6557