Development of a novel hybrid model (PDES–ANFIS) for time series applications

Most time series with a clear overall trend in their data and graphs require a model that effectively addresses the overall trend. If the time series also includes various fluctuations and random variations, nonlinear models are the ideal approach. To improve the prediction error and make it very small, a new model was applied to the time series of annual cancer cases in Iraq for the period from 1976 to 2023. This series contains a general trend covering more than 85% of the data, in addition to various random fluctuations and variations. The proposed hybrid model consists of two parts: the first part addresses the strong overall trend in a linear manner by partitioning the series into an optimal number of parts according to the optimal division that gives the lowest value for RMSE and MAPE, and applying a double exponential smoothing method to all parts to address the upward trend. The second part detects nonlinear patterns in the residuals of the first model using an adaptive network-based fuzzy inference system (ANFIS). The proposed hybrid model, Partitioned Double Exponential Smoothing (PDES-ANFIS), has proven to be more efficient compared to the unpartitioned hybrid model and single models by using the root mean square error (RMSE).