Khalil Ahmed Abdelreheem, Mandour Mohamed Abdelaziz, Ali Ahmed
School of Mathematics and Statistics, Central South University, Changsha, Hunan, China.
Faculty of Commerce, Assiut University, Assiut, Egypt.
PeerJ Comput Sci. 2024 Nov 26;10:e2500. doi: 10.7717/peerj-cs.2500. eCollection 2024.
Decision-making in many industries relies heavily on accurate forecasts, including the insurance sector. The Social Insurance System (SIS) in Egypt, operating under a fully funded paradigm, depends on reliable predictions to ensure effective financial planning. This research introduces a hybrid predictive model that combines fuzzy time series (FTS) Markov chains with the tree partition method (TPM) and difference transformation to forecast total pension benefits within Egypt's SIS. A key feature of the proposed model is its ability to optimize the partitioning process, resulting in the creation of nine intervals that reduce computational complexity while maintaining forecasting accuracy. These intervals were consistently applied across all fuzzy time series models for comparison. The model's performance is evaluated using established metrics such as MAPE, Thiels' U statistic, and RMSE. Additionally, prediction interval coverage probability (PICP) and mean prediction interval length (MPIL) are used to assess the quality of prediction intervals, with a 95% prediction interval serving as the baseline. The proposed model achieved a PICP of approximately 95%, indicating well-calibrated prediction intervals, although the MPIL of 424.5 reflects a wider uncertainty range. Despite this, the model balances coverage accuracy and interval precision effectively. The results demonstrate that the proposed model significantly outperforms traditional models like linear regression, ARIMA, and exponential smoothing and conventional FTS models like Song, Chen, Yu, and Cheng by achieving the lowest MAPE with the value of 11.8% for training and 10.65% for testing. This superior performance highlights the model's reliability and potential applicability to further forecasting tasks in the field of insurance and beyond.
许多行业的决策都严重依赖于准确的预测，保险行业也不例外。埃及的社会保险系统（SIS）在完全积累制模式下运行，依靠可靠的预测来确保有效的财务规划。本研究引入了一种混合预测模型，该模型将模糊时间序列（FTS）马尔可夫链与树划分方法（TPM）以及差分变换相结合，以预测埃及社会保险系统内的养老金总福利。所提出模型的一个关键特征是其能够优化划分过程，从而创建九个区间，在保持预测准确性的同时降低计算复杂度。这些区间在所有模糊时间序列模型中持续应用以进行比较。使用平均绝对百分比误差（MAPE）、泰尔U统计量和均方根误差（RMSE）等既定指标对模型的性能进行评估。此外，预测区间覆盖概率（PICP）和平均预测区间长度（MPIL）用于评估预测区间的质量，以95%的预测区间作为基线。所提出的模型实现了约95%的PICP，表明预测区间校准良好，尽管424.5的MPIL反映了较宽的不确定性范围。尽管如此，该模型有效地平衡了覆盖准确性和区间精度。结果表明，所提出的模型显著优于线性回归、自回归积分移动平均（ARIMA）和指数平滑等传统模型以及宋、陈、于和程等传统模糊时间序列模型，在训练时MAPE值为11.8%，测试时为10.65%，达到了最低值。这种卓越的性能突出了该模型的可靠性及其在保险及其他领域进一步预测任务中的潜在适用性。
