An Integrated Approach to Explore the Complexity of Interest Rates Network Structure

We represent the relationships among interest rates of the same term structure using an integrated approach, which combines quantile regression and graphs. First, the correlation matrix estimated via the quantile regression (QR) is used to explore the inner links among interest rates with different maturity. This lets us possible to check for quantile cointegration among short and long-term interest rates and to assess the Expectations Hypothesis of the term structure. Second, we use these inner links to build the Minimum Spanning Tree (MST) and we investigate the topological role of maturities as centres of a network, in an application focusing on the European interest rates term structure in the period 2006–2017. To validate our choice, we compare the MST built upon the quantile regression to the one based on the sample correlation matrix. The results highlight that the QR exalts the prominent role of short-term interest rates; moreover, the connections among interest rates of the same term structure seem being better captured and described by our procedure rather than by the methodology relying on the estimation of the sample correlation matrix.