“Testing the Stability of the Components Explaining Changes of the Yield Curve in Mexico. A Principal Component Analysis Approach”

A number of research works in finance rely on the selection of factors affecting the behaviour of one or more underlying variables. Factor Analysis (FA) and Principal Components Analysis (PCA) are statistical tools allowing for selecting a reduced number of factors explaining the variations of a set of variables. Of particular interest has been the study of the factors explaining the behaviour of the yield curve. It is well known that at least three factors are relevant for explaining variations in bonds and money market returns; these factors are level, slope and curvature. Financial practitioners use the set of components for portfolio hedging strategies. This document aims to test the stability of the factors over time. It is assumed that the factors change in a continuous time basis. Another hypothesis is that they are the same for a period but the variance explained for each one of them changes constantly. Technically, it means that the off-diagonal elements of a number of covariance matrices remain are the same but the diagonal elements are specific to each one of them. Three approaches were use to test the hypothesis of common principal components for the Mexican experience. The results are mixed and though in some cases they appear to support the hypothesis of stability of some of the factors, I found a number of problems, particularly computational and numerical, for appropriately testing it.