The dynamics of the term structure of interest rates: an Independent Component Analysis

Abstract

The movements of a term structure of interest rates are commonly assumed to be driven by a small number of uncorrelated factors. Identified to the level, the slope, and the curvature, these factors are routinely obtained by a Principal Component Analysis (PCA) of historical bond prices (interest rates). In this paper, we focus on the Independent Component Analysis (ICA). The central assumption here is that observed multivariate time series reflect the reaction of a system to some (few) statistically independent time series. The ICA seeks to extract out independent components (ICs) as well as the mixing process. Both ICA and PCA are linear transform of the observed series. But, whereas a PCA obtains uncorrelated (principal) components, ICA provides statistically independent components. In contrast to PCA algorithms that use only second order statistical information, ICA algorithms (like JADE) exploit higher order statistical information for separating the signals. This approach is required when financial data are suspected to be not gaussian.