TITLE:
Modeling Seasonal Fractionally Integrated Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroscedasticity Model with Seasonal Level Shift Intervention
AUTHORS:
Lawrence Dhliwayo, Florance Matarise, Charles Chimedza
KEYWORDS:
Seasonality, Fractional Integration, Long-Memory, Level Shift, SLS-SARFIMA, SLS-GARCH, Volatility
JOURNAL NAME:
Open Journal of Statistics,
Vol.10 No.5,
October
27,
2020
ABSTRACT: This paper introduces
the class of seasonal fractionally integrated autoregressive moving average-generalized conditional heteroskedastisticty
(SARFIMA- GARCH) models, with level shift type intervention that are capable of
capturing simultaneously four key features of time series: seasonality, long
range dependence, volatility and level shift. The main focus is on modeling
seasonal level shift (SLS) in fractionally integrated and volatile processes. A
natural extension of the seasonal level shift detection test of the mean for a
realization of time series satisfying SLS-SARFIMA and SLS-GARCH models was derived. Test
statistics that are useful to examine if seasonal level shift in an SARFIMA-GARCH model is statistically
plausible were established. Estimation of SLS-SARFIMA and SLS-GARCH parameters
was also considered.