摘要
This paper introduces the class of seasonal fractionally integrated autoregressive<span style="font-family:Verdana;"> moving average</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">generalized conditional heteroskedastisticty (SARFIMA-</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">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 w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> derived. Test statistics that are useful to examine if seasonal level shift in a</span><span style="font-family:Verdana;">n</span><span style="font-family:Verdana;"> SARFIMA-GARCH model </span><span style="font-family:Verdana;">is</span><span style="font-family:Verdana;"> statistically plausible were established. Estimation of SLS-SARFIMA and SLS-GARCH parameters w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> also considered.</span>
This paper introduces the class of seasonal fractionally integrated autoregressive<span style="font-family:Verdana;"> moving average</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">generalized conditional heteroskedastisticty (SARFIMA-</span><span style="font-family:;" "=""> </span><span style="font-family:Verdana;">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 w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> derived. Test statistics that are useful to examine if seasonal level shift in a</span><span style="font-family:Verdana;">n</span><span style="font-family:Verdana;"> SARFIMA-GARCH model </span><span style="font-family:Verdana;">is</span><span style="font-family:Verdana;"> statistically plausible were established. Estimation of SLS-SARFIMA and SLS-GARCH parameters w</span><span style="font-family:Verdana;">as</span><span style="font-family:Verdana;"> also considered.</span>
作者
Lawrence Dhliwayo
Florance Matarise
Charles Chimedza
Lawrence Dhliwayo;Florance Matarise;Charles Chimedza(Department of Statistics, University of Zimbabwe, Harare, Zimbabwe;School of Statistics and Actuarial Science, University of Witwatersrand, Johannesburg, South Africa)
