Tests for Jumps in Yield Spreads

Abstract

This article studies high-frequency econometric methods to test for a jump in the spread of bond yields. We propose a coherent inference procedure that detects a jump in the yield spread only if at least one of the two underlying bonds displays a jump. Ignoring this inherent connection by basing inference only on a univariate jump test applied to the spread tends to overestimate the number of jumps in yield spreads and puts the coherence of test results at risk. We formalize the statistical approach in the context of an intersection union test in multiple testing. We document the relevance of coherent tests and their practicability via simulations and real data examples.

KEYWORDS:

• Break-even inflation
• High-frequency data
• Intersection union test
• Jumps
• Sequential testing
• Term spread

Supplementary Materials

The supplementary materials contain technical assumptions and proofs, additional simulation results, and details of the bond data used for the empirical study.

Acknowledgments

The authors are grateful to the Editor, the Associate Editor, and two anonymous referees for helpful and constructive comments.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 For a zero coupon bond the relationship between yields, y_t, and prices, P_t, is $y_t^{(i)}=-\hspace{0.17em}\log \hspace{0.17em}{P}_t^{(i)}/m^{(i)}$, with time to maturity $m^{(i)},i=a,b$. Detecting jumps in the bond yields and bond prices are interchangeable. Given the focus of the article, we refer to yields directly instead of log-prices.

2 See, for example, Bibinger and Winkelmann (2018) and Li, Todorov, and Zhang (2021), for studies on jumps in (co)volatility.

3 Incoherent test outcomes are a subset of rejections at the rejection boundary. The smaller the α, the more extreme we are in the tails of bivariate return distributions, and the fewer conflicting statistics are detectable. A potential degeneracy is the consequence of data limitation far in the tail, and not because the incoherent test results do not exist for small local α. In fact, the simulation results in Figure 3 demonstrate that incoherent test outcomes become more likely with smaller α.

Additional information

Funding

Winkelmann acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG) project number 363880538. Winkelmann and Yao also acknowledge financial support from the Australian Research Council Discovery Grants Program (DP220100321).