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arxiv: 2409.00348 · v2 · submitted 2024-08-31 · 💱 q-fin.ST

State-Space Dynamic Functional Regression for Multicurve Fixed Income Spread Analysis and Stress Testing

Peilun He , Gareth W. Peters , Nino Kordzakhia , Pavel V. Shevchenko This is my paper

Pith reviewed 2026-05-23 21:16 UTC · model grok-4.3

classification 💱 q-fin.ST
keywords Nelson-Siegel modelfunctional regressionyield curvestate-space modelspread analysisstress testingfixed incomekernel PCA
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The pith

State-space functional regression extends Nelson-Siegel to model yield spreads between economies.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a state-space functional regression model that combines dynamic Nelson-Siegel yield curve dynamics with functional regression in a multi-economy setting. This framework is designed to explain relative spreads in yields between a reference economy and a response economy. Kernel principal component analysis reduces the functional problem to a finite-dimensional estimation task. The model is evaluated through in-sample comparisons with the standard dynamic Nelson-Siegel model and applied to stress testing of yield curves using US and UK bond data for bond ladder portfolios.

Core claim

A novel state-space functional regression model incorporating dynamic Nelson-Siegel and functional regression formulations in a multi-economy setting offers distinct advantages in explaining the relative spreads in yields between a reference economy and a response economy, made tractable by kernel principal component analysis.

What carries the argument

State-space dynamic functional regression model with dynamic Nelson-Siegel components and kernel principal component analysis for finite-dimensional transformation.

If this is right

  • The functional regression approach shows advantages in explaining yield spreads over the dynamic Nelson-Siegel model in in-sample performance.
  • The framework supports stress testing analysis of yield curve term-structures in a dual economy setting.
  • Bond ladder portfolios can be examined through spread modelling with historical US Treasury and UK bond data.
  • Model calibration is addressed by transforming functional regression into a tractable finite-dimensional problem.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The model structure may allow extension to additional economies beyond the dual reference-response setup.
  • Applications to other fixed income instruments with similar curve dynamics could follow from the same state-space formulation.
  • Real-time updating of spread forecasts might be enabled by the state-space nature of the model.

Load-bearing premise

Kernel principal component analysis transforms the functional regression representation into a finite-dimensional tractable estimation problem without material loss of information or introduction of bias in the spread dynamics.

What would settle it

Empirical results where the state-space functional regression model does not demonstrate superior in-sample fit or stress testing performance compared to the dynamic Nelson-Siegel model on the US and UK yield data.

Figures

Figures reproduced from arXiv: 2409.00348 by Gareth W. Peters, Nino Kordzakhia, Pavel V. Shevchenko, Peilun He.

Figure 1
Figure 1. Figure 1: Factor loadings of the DNS model with 𝜆 = 0.0609. with the level, slope, and curvature of the Nelson-Siegel model, highlighting the versatility and adaptability of FDA in capturing the complex dynamics of yield curves. The applications of FDA in the interest rate market was explored in [44] and [45]. It is noteworthy that, in reality, data is often incomplete. In the presence of missing data, bootstrapping… view at source ↗
Figure 2
Figure 2. Figure 2: UK yield curves from January 2010 to December 2020. The left figure is for the original data, and the right figure is for the data after maturity matching. 9-month yield and 7-year (84-month) yield are interpolated in the right figure. 7. Empirical Analysis In this section, we present the empirical results. We first show the in-sample estimations using the DNS model and the DNS-FR model in Section 7.1 and … view at source ↗
Figure 3
Figure 3. Figure 3: Estimated UK yield curves by DNS model and DNS-FR model on three different months. 7.3. Forecasting In this section, we compare the performance of the DNS model and the DNS-FR model in out-of-sample forecasting, using the methods discussed in Section 5. Forecast accuracy is evaluated using the RMSE for 12-step ahead (ℎ = 12) forecasts. Tables 3 and 4 present the RMSE for the DNS model and the DNS-FR model,… view at source ↗
Figure 4
Figure 4. Figure 4: In-sample and out-of-sample mean RMSE for UK yields using a 5-year moving window, move forward for 1 month each time. The date of each point represents the middle date of the moving window. 7.4. Stress Testing In this section, we conduct a stress testing analysis to answer the following question: If different shocks are applied to the US Treasury market, how do the bond markets of other countries/regions r… view at source ↗
Figure 5
Figure 5. Figure 5: Mean difference in percentage points of in-sample estimations between stress testing scenario 1 and original data for UK yields. The mean values are taken over short-end ((0, 5] years), middle ((5, 10] years), and long-end ( (10, 30] years) maturities. Dashed lines represent the lower and upper bounds of 95% confidence interval for each curve. 1-year, 2-year, and 3-year US Treasury. The effects of the midd… view at source ↗
Figure 6
Figure 6. Figure 6: Mean difference in percentage points of in-sample estimations between stress testing scenario 2 and original data for UK yields. The mean values are taken over short-end ((0, 5] years), middle ((5, 10] years), and long-end ( (10, 30] years) maturities. Dashed lines represent the lower and upper bounds of 95% confidence interval for each curve. (a) Functional coefficient for original data. (b) Functional co… view at source ↗
Figure 7
Figure 7. Figure 7: Functional coefficients for UK yields. 7.5. Case Study: Bond Ladder Portfolio In this section, we present a case study of a bond ladder portfolio for risk management purposes. A bond ladder portfolio can be described as follows. Assume a US investor wants to construct an investment strategy consisting of cash and a UK bond with a maturity of 𝑇 months. At time 𝑡 𝑖 , the investor spends 𝑝𝑖 dollars to purchas… view at source ↗
Figure 8
Figure 8. Figure 8: illustrates the entire process of constructing the bond ladder portfolio. Time t t0 t0 + T p0 t1 t1 + T p1 t2 t2 + T p2 · · · . . . tk tk + T pk 1 [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Predicted portfolio values [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Differences of portfolio values between each stress testing scenario and original data, for different maturity of the underlying bond. shows the 5% VaR for the portfolio value of bonds with 6-month, 1-year, and 30-year maturities, which is calculated numerically. At the end of 12 months, the 5% VaR of the portfolio values of the 6-month and 1-year bonds are roughly $12.5 and $12.7 million, respectively, i… view at source ↗
Figure 11
Figure 11. Figure 11: 5% value-at-risk (VaR) for bond ladder portfolios with different maturities [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Differences of 5% value-at-risk (VaR) between each stress testing scenario and original data, for different maturity of the underlying bond. 8. Conclusion The dynamic Nelson-Siegel (DNS) model has been pivotal in yield curve estimation over the past two decades. However, it falls short in capturing the relative spread between two economies. In this paper, we introduce a novel dynamic Nelson-Siegel functio… view at source ↗
Figure 13
Figure 13. Figure 13: In-sample and out-of-sample mean RMSE for France yields using a 5-year moving window, move forward for 1 month each time. (a) In-sample mean RMSE. (b) Out-of-sample mean RMSE [PITH_FULL_IMAGE:figures/full_fig_p029_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: In-sample and out-of-sample mean RMSE for Italy yields using a 5-year moving window, move forward for 1 month each time. Peilun He et al.: Preprint submitted to Elsevier Page 29 of 35 [PITH_FULL_IMAGE:figures/full_fig_p029_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: In-sample and out-of-sample mean RMSE for Germany yields using a 5-year moving window, move forward for 1 month each time. (a) In-sample mean RMSE. (b) Out-of-sample mean RMSE [PITH_FULL_IMAGE:figures/full_fig_p030_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: In-sample and out-of-sample mean RMSE for Japan yields using a 5-year moving window, move forward for 1 month each time. (a) In-sample mean RMSE. (b) Out-of-sample mean RMSE [PITH_FULL_IMAGE:figures/full_fig_p030_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: In-sample and out-of-sample mean RMSE for Australia yields using a 5-year moving window, move forward for 1 month each time. Peilun He et al.: Preprint submitted to Elsevier Page 30 of 35 [PITH_FULL_IMAGE:figures/full_fig_p030_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: In-sample and out-of-sample mean RMSE for EU yields using a 5-year moving window, move forward for 1 month each time. Peilun He et al.: Preprint submitted to Elsevier Page 31 of 35 [PITH_FULL_IMAGE:figures/full_fig_p031_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Time series of original US Treasury bond yields. (a) Case 1.1 (b) Case 1.2 (c) Case 1.3 (d) Case 1.4 [PITH_FULL_IMAGE:figures/full_fig_p032_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Time series of US Treasury bond yields for stress testing scenario 1. Peilun He et al.: Preprint submitted to Elsevier Page 32 of 35 [PITH_FULL_IMAGE:figures/full_fig_p032_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Time series of US Treasury bond yields for stress testing scenario 2. CRediT authorship contribution statement Peilun He: Software, Validation, Investigation, Formal analysis, Writing - Original Draft, Writing - Review & Editing, Visualization. Gareth W. Peters: Conceptualization, Investigation, Methodology, Formal Analysis, Software, Writing - Original Draft, Writing - Review & Editing, Supervision. Nino… view at source ↗
read the original abstract

The Nelson-Siegel model is widely used in fixed income markets to produce yield curve dynamics. The multiple time-dependent parameter model conveniently addresses the level, slope, and curvature dynamics of the yield curves. In this study, we present a novel state-space functional regression model that incorporates a dynamic Nelson-Siegel model and functional regression formulations applied to multi-economy setting. This framework offers distinct advantages in explaining the relative spreads in yields between a reference economy and a response economy. To address the inherent challenges of model calibration, a kernel principal component analysis is employed to transform the representation of functional regression into a finite-dimensional, tractable estimation problem. A comprehensive empirical analysis is conducted to assess the efficacy of the functional regression approach, including an in-sample performance comparison with the dynamic Nelson-Siegel model. We conducted the stress testing analysis of yield curves term-structure within a dual economy framework. The bond ladder portfolio was examined through a case study focused on spread modelling using historical data for US Treasury and UK bonds.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a state-space dynamic functional regression framework that integrates the dynamic Nelson-Siegel model with functional regression to analyze yield curve spreads between a reference economy and a response economy. Kernel principal component analysis reduces the functional regressors to a finite-dimensional estimation problem. The approach is evaluated via in-sample comparisons against dynamic Nelson-Siegel on US/UK data, stress testing of term structures, and a bond-ladder portfolio case study focused on spread modeling.

Significance. If the KPCA reduction preserves the relevant Nelson-Siegel factor dynamics without material bias, the model could improve multicurve spread analysis and stress testing relative to standard dynamic Nelson-Siegel alone. The dual-economy empirical application and portfolio case study provide concrete illustrations of potential practical utility in fixed-income risk management.

major comments (2)
  1. [Abstract and §3] Abstract and §3: The central claim of distinct advantages in explaining relative US-UK yield spreads hinges on the KPCA step producing a finite-dimensional representation without material loss of information or bias in spread dynamics. No evidence is supplied (e.g., sensitivity checks on kernel bandwidth, retained component count, or comparison of factor loadings before/after projection) that truncation does not distort curvature or slope components that drive the spreads; this directly affects the estimated state transitions and stress-test outputs.
  2. [Empirical analysis section] Empirical analysis section: The in-sample performance comparison with the dynamic Nelson-Siegel model reports no error bars, out-of-sample hold-out results, or controls for data-driven choices of KPCA hyperparameters, leaving open whether any reported improvement in spread fit is robust or an artifact of in-sample overfitting.
minor comments (1)
  1. Notation for the state-space transition matrices and observation equations should explicitly distinguish reference-economy versus response-economy quantities to avoid ambiguity when spreads are formed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the KPCA validation and empirical robustness. We address each point below and will revise the manuscript accordingly to strengthen the supporting evidence.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3: The central claim of distinct advantages in explaining relative US-UK yield spreads hinges on the KPCA step producing a finite-dimensional representation without material loss of information or bias in spread dynamics. No evidence is supplied (e.g., sensitivity checks on kernel bandwidth, retained component count, or comparison of factor loadings before/after projection) that truncation does not distort curvature or slope components that drive the spreads; this directly affects the estimated state transitions and stress-test outputs.

    Authors: We agree that the manuscript currently lacks explicit sensitivity checks on the KPCA step. In the revised version, we will add analyses varying kernel bandwidth and retained component count, along with direct comparisons of Nelson-Siegel factor loadings before and after projection. These additions will demonstrate that truncation does not materially distort slope and curvature dynamics relevant to spreads, thereby supporting the state transitions and stress-test results. revision: yes

  2. Referee: [Empirical analysis section] Empirical analysis section: The in-sample performance comparison with the dynamic Nelson-Siegel model reports no error bars, out-of-sample hold-out results, or controls for data-driven choices of KPCA hyperparameters, leaving open whether any reported improvement in spread fit is robust or an artifact of in-sample overfitting.

    Authors: The current empirical section presents in-sample comparisons primarily for illustrative purposes. We acknowledge that this leaves the robustness open to question. In revision, we will incorporate out-of-sample hold-out evaluations, report error bars or confidence intervals on performance metrics, and document plus test sensitivity to KPCA hyperparameter choices to rule out overfitting artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation remains independent of fitted inputs

full rationale

The paper introduces a state-space functional regression that augments dynamic Nelson-Siegel factors with functional regressors across economies, then applies KPCA solely for computational tractability. No equation or step in the provided text defines the target spreads in terms of the same fitted quantities used for estimation, nor does any prediction reduce by construction to a parameter fit on the identical data. The in-sample comparison to the baseline Nelson-Siegel model is a standard benchmark evaluation rather than a self-referential claim. Self-citations are absent from the abstract and description, and the KPCA step is presented as an approximation tool without any uniqueness theorem or ansatz imported from prior author work. The central claim of improved spread explanation therefore rests on external empirical performance rather than definitional equivalence.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits ledger to explicitly invoked components; dynamic Nelson-Siegel time-dependent parameters are standard but fitted, and kernel PCA is invoked as a reduction step whose accuracy is assumed.

free parameters (1)
  • Dynamic Nelson-Siegel time-dependent parameters
    Level, slope, and curvature factors are time-varying and calibrated to yield data in the model.
axioms (1)
  • domain assumption Kernel principal component analysis accurately reduces functional regression to finite dimensions without significant information loss for spread modeling.
    Invoked to address calibration challenges and enable tractable estimation.

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