Lee-Carter model and Kernel PCA

Abstract

This thesis investigates the application of Kernel Principal Component Analysis (KPCA) method on the Lee-Carter model, which is a two-step model for estimating and forecasting mortality rates (Lee and Carter, 1992). The motivation comes from the possible non-linearity of mortality data which cannot be captured by the traditional SVD and MLE methods. The proposed KPCA Lee-Carter model maps the mortality data into the feature space using kernel functions. Experiments on various kernels are conducted. The kernel and its corresponding parameters with the lowest forecasting error in k-fold cross validation are selected. The empirical analysis is conducted on U.S. mortality data to evaluate the model performance and simulation study is conducted to prove model correctness.