ABSTRACT
Most time series are characterized in practice that they consist of two components, linear and nonlinear, and when making predictions, the single models are not sufficient to model these series. Recently several linear, non-linear and hybrid models have been proposed for prediction, In this research, a new hybrid model was proposed based on the combination of the linear model Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) with the non-linear model fuzzy time series model (FTS). The proposed hybrid model analyzes the linear component of the specified time series using the ARFIMA model, calculates the estimated values, and then calculates the residuals for this model by subtracting the estimated values from the original time series. The nonlinear component is analyzed using the (FTS) model for the computed residuals, which inherently contain the nonlinear patterns of the time series. The final values for the prediction by applying the hybrid model (ARFIMA-FTS) are obtained by combining the predictions of the (ARFIMA) model of the original series with the predictions of the model (FTS) for the residual series. The new hybrid model was used to predict those infected with Covid-19 virus in Iraq for the period from 24/2/2020 to 11/8/2021. The proposed model was more efficient in the prediction process than the single (ARFIMA) model using a number of comparison criteria, including (RMSE), (MAPE) and (MAE). The final results showed that the proposed model has the ability to predict time series that contain linear and nonlinear components.