In an economy with multiple sources of risk, the short-term interest rate does not capture all the information that determines the conditional distribution of bond yields. This is also true for path-dependent term structure models. In either case, the current short rate level is not a sufficient statistic for the conditional density of future short rates. This paper studies the empirical relevance of both issues from a time-series nonparametric perspective. The analysis is formulated as a test for the dependence of the short rate drift and diffusion on variables other than the short rate, and exploits Ait-Sahalia, Bickel, and Stocker (2001) dimension reduction method. The paper explores the finite sample performance of the method and applies the test to US interest rate data. Results reject a single-factor Markovian model, although conclusions are sensitive to the choice of additional conditioning variables.
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