Seasonal Fractional ARIMA model with BL-GARCH type innovations

Mor Ndongo (1) , Abdou Kâ Diongue (2) , Simplice Dossou-Gbété (3)

1 Lerstad
2 LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement
3 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

In this paper, we introduce the class of seasonal ARFIMA models with bilinear GARCH (BL-GARCH) type innovations that are capable of capturing simultaneously four key properties of non-linear time series: long range dependence, seasonality, volatility clustering and leverage effects. Stationarity and invertibility conditions are derived and conditional sum of squares (CSS) estimation of the model is also considered. Under some assumptions, we show that the resulting estimators are consistent and asymptotically normally distributed. Monte carlo simulation results are presented to evaluate the small-sample performance of the CSS method for various models.

Mots clés: Long memory; Seasonality; Leverage effects; CSS method; Monte Carlo experiments; Volatility clustering

Domaines: Méthodes et statistiques; Statistiques [stat]

Mor Ndongo, Abdou Kâ Diongue, Simplice Dossou-Gbété. Seasonal Fractional ARIMA model with BL-GARCH type innovations. 2015. ⟨hal-01121437⟩