Fourier Estimation Method Applied to Forward Interest Rates

Principal component analysis (PCA) is a general method to analyse the factors of the term structure of interest rates. There are usually two or three factors. However, it is shown by Liu that when we apply PCA to forward rates, not spot rates, we need more factors to explain 95% of variability. In order to verify the robustness of this result, we introduce another method based on Fourier series, which is proposed by Malliavin and Mancino. The results reconfirm the observation of Liu with different data sets. In particular, the Fourier series method gives us similar results to PCA.