Wavelet theory is known to be a powerful tool for compressing and processing time series or images. It consists in projecting a signal on an orthonormal basis of functions that are chosen in order to provide a sparse representation of the data. The first part of this article focuses on smoothing mortality curves by wavelets shrinkage. A chi-square test and a penalized likelihood approach are applied to determine the optimal degree of smoothing. The second part of this article is devoted to mortality forecasting. Wavelet coefficients exhibit clear trends for the Belgian population from 1965 to 2015, they are easy to forecast resulting in predicted future mortality rates. The wavelet-based approach is then compared with some popular actuarial models of Lee–Carter type estimated fitted to Belgian, UK, and US populations. The wavelet model outperforms all of them.

众所周知，小波理论是压缩和处理时间序列或图像的强大工具。它包括在正交函数的基础上投影信号，这些函数是为了提供数据的稀疏表示而选择的。本文的第一部分着重于通过小波收缩平滑死亡率曲线。应用卡方检验和惩罚似然法来确定最佳平滑度。本文的第二部分专门介绍死亡率预测。小波系数在1965年至2015年期间显示了比利时人群的明显趋势，易于预测，可预测未来的死亡率。然后将基于小波的方法与估计适用于比利时，英国和美国人口的一些流行的Lee-Carter型精算模型进行比较。