Investigating Rainfall Persistence in the Seybouse Watershed of Northeastern Algeria using the ARFIMA model

This research paper examines the persistence of precipitation forecast memory by estimating the fractional differentiation parameter (d) of the AutoRegressive Fractionally Integrated Moving Average (AutoRegressive Fractionally Integrated Moving Average (ARFIMA)) model and the corresponding Hurst exponent (H) using the maximum likelihood method (LM) and nonlinear least squares estimation method (NLS). The optimal method is selected based on criteria such as minimal AIC, portmanteau, and residue tests. The study focuses on monthly rainfall data from four representative stations in the Seybouse watershed area in the Algerian Northeast, covering the period from January 1, 1998, to December 31, 2007. To ensure data normality, the Cox-Box transformation is applied to model the studied process. The constructed Autoregressive Fractionally Integrated Moving Average (ARFIMA) models exhibit the following characteristics: Annaba station: (5; 0.13; 14) with a Hurst exponent (H) of 0.63, indicating long forecast memory; Oum El Bouaghi station: (0; 0.11; 0) with (H) of 0.61, indicating long forecast memory; Guelma station: (9; -0.16; 4) with (H) of 0.34, indicating long forecast memory; and Souk Ahras station: (2; -0.37; 2) with (H) of 0.13, indicating anti-persistence.