A comparative study of principal component analysis on term structure of interest rates

Abstract

In this paper, principal component analysis (PCA) is applied to three different parametrization of interest rates: zero rates, yield curve, and forward rates. This comparative study is complementary to Akahori, Aoki, and Nagata \cite{AAN06} where they claimed that, under the no-arbitrage principle, yield curve cannot be a random walk. Conversely the forward curve could be a random walk. In our result of PCA, however, we observed that of the general beliefs. Our empirical results on the number of factors for the zero rates and the yield curve align with the general beliefs. This is a puzzle.