Modeling Seasonal Fractionally Integrated Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroscedasticity Model with Seasonal Level Shift Intervention

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.

Linear frequency modulated reverberation suppression using time series models

“…Noise reduction, speech and audio signal augmentation, hydrology, dendrochronology, econometrics, and other fields regularly use ARMA. The overlapping of many LFM reflection signals causes reverberation [21]- [24]. The autoregression and moving average (ARMA) models are used in time series analysis to characterise stationary time series.…”