Jiajing Sun

Jiajing Sun

PhD, CFA charterholder, FIMA, Member of the London Mathematical Society. Associate Professor and the Deputy Director of the Department of Statistics and Data Science, School of Economics and Management, University of the Chinese Academy of Sciences.

A Nonparametric Test for Omitted State Variables in Interest-Rate Volatility

Published:

Status: Updated Journal of Financial Econometrics submission version, 2026.

Authors:

Fuchun Li, Jiajing Sun, and Yuanlin Wang.

This working paper studies omitted-state-variable testing for interest-rate volatility. The central question is whether a candidate state variable can be omitted from a conditional variance function after conditioning on retained state variables. The null is not homoskedasticity and not a parametric volatility restriction; it asks whether the reduced volatility information set is adequate.

Summary and Contribution:

The paper proposes a nonparametric omitted-state-variable test for conditional variance functions. The statistic compares full and reduced kernel variance estimators through a weighted distance measure, with bias correction and studentization.

Under the null, the standardized statistic is asymptotically standard normal. The test is consistent against fixed alternatives and has nontrivial local power. The theory is complemented by Monte Carlo experiments documenting finite-sample size and power.

Empirical Illustration:

The empirical application uses daily Canadian interest-rate data. The response is the scaled one-day change in the 3-month Government of Canada Treasury bill rate. The retained volatility state is the current 3-month rate, and the candidate omitted state is the 10-year Government of Canada benchmark bond yield.

The test rejects omitting the 10-year yield as an additional term-structure state across sample windows, support choices, and both asymptotic and bootstrap critical values. The evidence is interpreted as information about the volatility information set, not as a structural causal effect of the long rate on short-rate volatility.

Keywords:

Conditional variance function; interest-rate volatility; nonparametric specification test; omitted variables; short-rate models; U-statistics.

Availability:

The manuscript and online supplement are not hosted on this website due to copyright and journal submission policy. Presentation slides are available for download: Slides (PDF).