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arxiv: 2606.26815 · v1 · pith:D3KQMAHZnew · submitted 2026-06-25 · 💱 q-fin.PM · q-fin.CP· stat.ML

Data-Driven Duration Management -- Term Structure Forecasting Using Machine Learning

Tobias Lausser , Joao Eduardo Vuolo , Rudi Zagst This is my paper

Pith reviewed 2026-06-26 01:48 UTC · model grok-4.3

classification 💱 q-fin.PM q-fin.CPstat.ML
keywords term structure forecastingneural networksyield curvemachine learningdynamic Nelson-Siegelprincipal component analysisbond portfoliozero rates
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The pith

Neural networks that integrate factor models outperform classical econometric approaches in forecasting U.S. and European government bond yield curves.

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

The paper compares classical models such as the Dynamic Nelson-Siegel model and Principal Component Analysis with various neural network architectures for predicting the term structure of zero-coupon government bonds in the United States and Europe. It evaluates these methods using both statistical metrics like RMSE and MAE and the economic performance of a quantitative bond trading strategy. Neural networks are shown to deliver better forecasting accuracy and higher portfolio returns than traditional models. The best performing models differ by region, with a direct-forecasting neural network incorporating DNS factors and an autoencoder for macroeconomic features working best for the U.S., while a factor-based neural network using PCA factors without macroeconomic variables is optimal for Europe.

Core claim

Neural networks consistently outperform traditional models in both forecasting accuracy and portfolio performance. For the U.S., the most effective approach is a direct-forecasting NN that incorporates DNS factors to reduce the dimensionality of zero-rate data and an Autoencoder to extract macroeconomic features, while for Europe, the optimal model is a factor-based NN using PCA-derived zero-rate factors without the integration of macroeconomic variables.

What carries the argument

Neural network architectures that blend classical factor models like DNS and PCA with machine learning techniques for dimensionality reduction and feature extraction.

If this is right

  • Neural networks improve both statistical forecasting accuracy and the returns from quantitative bond trading strategies.
  • Different optimal model configurations apply to the U.S. Treasury market versus the European market.
  • Macroeconomic variables enhance neural network performance in the U.S. but are not beneficial in Europe.
  • Combining traditional term structure models with modern machine learning supports better fixed-income portfolio construction.

Where Pith is reading between the lines

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

  • These findings could support more effective duration management in bond portfolios by providing better yield curve forecasts.
  • Similar machine learning approaches might be tested on corporate bonds or other fixed-income assets.
  • The model evaluation framework combining statistical and economic metrics could be applied to other forecasting problems in finance.

Load-bearing premise

The reported outperformance reflects genuine predictive power rather than overfitting to the specific sample periods or data choices, and the quantitative trading strategy evaluation accurately captures economic value without look-ahead bias.

What would settle it

Re-running the analysis on data from a subsequent period not included in the original sample to check if the neural network models maintain their advantage in forecasting accuracy and trading performance.

Figures

Figures reproduced from arXiv: 2606.26815 by Joao Eduardo Vuolo, Rudi Zagst, Tobias Lausser.

Figure 1
Figure 1. Figure 1: U.S. zero-rate curve between April 1987 and February 2025. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Euro triple A zero-rate and German zero-rate curves between February 1992 and [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: DNS factor loadings with λt = 0.0606 for different times to maturity, T − t. Alternatively, we can use Principal Component Analysis (PCA) for dimensionality reduction. Unlike the DNS model, which imposes a specific functional form based on financial intuition, PCA is purely data-oriented. To maintain consistency, we retain the first three components for 9 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: PCA factor loadings for different times to maturity, [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Single-layered Autoencoder. While the DNS model provides an intuitive and flexible way to describe the shape and dynamics of the zero-rate curve, it does not prevent the possibility of arbitrage — that is, the existence of risk-free profit opportunities arising from inconsistencies in asset prices. In real financial markets, such situations should not persist: if they existed, traders would immediately exp… view at source ↗
Figure 6
Figure 6. Figure 6: Normalized latent factors fitted for the U.S. data with DNS, PCA, AE, and AFNS [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Architecture for the model employing NN for factor forecasting with a horizon [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Architecture for the model employing NN for direct zero-rate forecasting for horizon [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: AE for factor extraction of the zero-rate curve with architecture 7-3-7. [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: AE for factor extraction of the zero-rate curve with architecture 7-5-3-5-7. [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Box plots for the U.S. results depicting RMSE, MAE, directional accuracy across all [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Box plots for the Europe results depicting RMSE, MAE, directional accuracy across [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The first panel illustrates the portfolio duration implied by Model B31 based on [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The first panel illustrates the portfolio duration implied by Model N16 based on [PITH_FULL_IMAGE:figures/full_fig_p028_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparison between the one-month forecasts of Models N2, N5, and the actual U.S. [PITH_FULL_IMAGE:figures/full_fig_p031_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Comparison between the one-month forecasts of Models N16 and N32 and the actual [PITH_FULL_IMAGE:figures/full_fig_p031_16.png] view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: Performance from the different models and the benchmark between July 2014 [PITH_FULL_IMAGE:figures/full_fig_p047_3_1.png] view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Duration from the different portfolios between July 2014 and February 2025. [PITH_FULL_IMAGE:figures/full_fig_p048_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: Performance from the different models and the benchmark between December [PITH_FULL_IMAGE:figures/full_fig_p048_3_3.png] view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: Duration from the different portfolios in Europe between December 2014 and [PITH_FULL_IMAGE:figures/full_fig_p049_3_4.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Performance of the different portfolios between July 2014 and February 2018. [PITH_FULL_IMAGE:figures/full_fig_p050_4_1.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Duration of the different portfolios between July 2014 and February 2018. [PITH_FULL_IMAGE:figures/full_fig_p050_4_2.png] view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: Performance of the different portfolios between February 2018 and July 2021. [PITH_FULL_IMAGE:figures/full_fig_p051_4_3.png] view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: Duration of the different portfolios between February 2018 and July 2021. [PITH_FULL_IMAGE:figures/full_fig_p052_4_4.png] view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Performance of the different portfolios between July 2021 and November 2022. [PITH_FULL_IMAGE:figures/full_fig_p053_4_5.png] view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Duration of the different portfolios between July 2021 and November 2022. [PITH_FULL_IMAGE:figures/full_fig_p053_4_6.png] view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: Performance of the different portfolios between November 2022 and February [PITH_FULL_IMAGE:figures/full_fig_p054_4_7.png] view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: Duration of the different portfolios between November 2022 and February [PITH_FULL_IMAGE:figures/full_fig_p055_4_8.png] view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Performance of the different portfolios between December 2014 and September [PITH_FULL_IMAGE:figures/full_fig_p056_5_1.png] view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Duration of the different portfolios between December 2014 and September [PITH_FULL_IMAGE:figures/full_fig_p056_5_2.png] view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: Performance of the different portfolios between September 2019 and November [PITH_FULL_IMAGE:figures/full_fig_p057_5_3.png] view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: Duration of the different portfolios between September 2019 and November [PITH_FULL_IMAGE:figures/full_fig_p058_5_4.png] view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: Performance of the different portfolios between December 2021 and October [PITH_FULL_IMAGE:figures/full_fig_p059_5_5.png] view at source ↗
Figure 5.6
Figure 5.6. Figure 5.6: Duration of the different portfolios between December 2021 and October 2023. [PITH_FULL_IMAGE:figures/full_fig_p059_5_6.png] view at source ↗
Figure 5.7
Figure 5.7. Figure 5.7: Performance of the different portfolios between October 2023 and February [PITH_FULL_IMAGE:figures/full_fig_p060_5_7.png] view at source ↗
Figure 5.8
Figure 5.8. Figure 5.8: Duration of the different portfolios between October 2023 and February 2025. [PITH_FULL_IMAGE:figures/full_fig_p061_5_8.png] view at source ↗
read the original abstract

This paper compares different methods for forecasting the term structure of U.S. and European zero-coupon government bonds using both traditional econometric and Machine Learning (ML) approaches. We compare classical models (e.g., Dynamic Nelson-Siegel (DNS) and Principal Component Analysis (PCA)) with different Neural Network (NN) architectures, including those inspired by the classical models, on the U.S. Treasury market and bonds issued by the European Central Bank (ECB). To enhance predictive performance, macroeconomic variables are incorporated. The findings for both markets are separately analyzed and compared. To this end, we propose a robust model evaluation framework combining statistical accuracy metrics - such as RMSE, MAE, and directional accuracy - with the economic relevance of a quantitative bond trading strategy. Results show that NNs consistently outperform traditional models in both forecasting accuracy and portfolio performance. For the U.S., the most effective approach is a direct-forecasting NN that incorporates DNS factors to reduce the dimensionality of zero-rate data and an Autoencoder (AE) to extract macroeconomic features, while for Europe, the optimal model is a factor-based NN using PCA-derived zero-rate factors without the integration of macroeconomic variables. Overall, the paper demonstrates how combining traditional modeling approaches with modern ML techniques and evaluation can improve yield curve forecasts and support applications in fixed-income portfolio construction.

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 / 0 minor

Summary. The paper compares classical term structure models (Dynamic Nelson-Siegel and PCA) against multiple neural network architectures for forecasting US Treasury and ECB zero-coupon yields. Macroeconomic variables are added as inputs. Models are assessed via RMSE, MAE, directional accuracy, and the economic performance of a quantitative bond trading strategy. The central claim is that NNs consistently outperform the baselines, with a direct-forecasting NN (DNS factors + autoencoder for macros) optimal for the US and a factor-based NN (PCA zero-rate factors, no macros) optimal for Europe.

Significance. If the outperformance survives rigorous out-of-sample validation and controls for data snooping, the integration of classical factor structures with ML could improve yield-curve forecasting and fixed-income portfolio construction. The dual statistical-plus-economic evaluation metric is a constructive feature.

major comments (2)
  1. [Abstract] Abstract and evaluation framework: the manuscript asserts a 'robust model evaluation framework' yet supplies no concrete description of cross-validation, walk-forward hyperparameter selection, fixed training windows, or adjustments for multiple testing across architectures, factor choices, and macro inclusions. This is load-bearing for the claim of consistent NN superiority, as the results remain vulnerable to overfitting and look-ahead bias.
  2. [Evaluation framework] Trading-strategy evaluation: because portfolio returns are computed directly from the forecasts, the paper must demonstrate that the strategy metric is free of look-ahead bias and that any hyperparameter tuning for the NNs was performed without using information from the evaluation period.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for highlighting the need for greater transparency in our evaluation procedures. We agree that explicit documentation of cross-validation, walk-forward selection, and bias controls is essential to support the robustness claims. Below we address each major comment and commit to expanding the relevant sections in revision.

read point-by-point responses

  1. Referee: [Abstract] Abstract and evaluation framework: the manuscript asserts a 'robust model evaluation framework' yet supplies no concrete description of cross-validation, walk-forward hyperparameter selection, fixed training windows, or adjustments for multiple testing across architectures, factor choices, and macro inclusions. This is load-bearing for the claim of consistent NN superiority, as the results remain vulnerable to overfitting and look-ahead bias.

    Authors: We acknowledge that the current manuscript provides only a high-level reference to the evaluation framework without sufficient procedural detail. In the revised version we will add a dedicated subsection that specifies: (i) a rolling walk-forward scheme with fixed-length training windows ending at each forecast origin, (ii) hyperparameter selection performed exclusively via inner cross-validation on the training window (no test-period information), and (iii) a Bonferroni-style adjustment for the finite set of architectures and macro inclusions examined. These additions will be placed in both the methodology and results sections. revision: yes

  2. Referee: [Evaluation framework] Trading-strategy evaluation: because portfolio returns are computed directly from the forecasts, the paper must demonstrate that the strategy metric is free of look-ahead bias and that any hyperparameter tuning for the NNs was performed without using information from the evaluation period.

    Authors: We agree that explicit safeguards against look-ahead bias in the trading-strategy metric are required. The revised manuscript will include a new paragraph in the economic-evaluation section stating that (a) all positions are formed using only forecasts generated from models trained up to the rebalancing date, (b) transaction costs and slippage are applied at the subsequent period's realized prices, and (c) hyperparameter grids were optimized solely on the in-sample training folds with no leakage from the out-of-sample evaluation window. We will also report the exact training-window lengths and rebalancing frequency used. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper performs an empirical out-of-sample comparison of NN architectures against DNS and PCA baselines on RMSE/MAE/directional accuracy plus a separate quantitative bond trading strategy whose returns are computed from the forecasts. No equations, derivations, or self-citations are shown that reduce any claimed prediction or uniqueness result to a fitted input or prior author work by construction. The evaluation metrics and trading performance are independent of the model-fitting objective, satisfying the default expectation of a non-circular empirical study.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the work is purely empirical comparison.

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discussion (0)

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    Model Learning Rate Activation Function Batch Size Number of Lay- ers Neurons in Layer 1 Neurons in Layer 2 Epochs 8 0.001530 tanh 54 1 6 0 2000 9 0.005330 ReLu 30 1 4 0 2000 10 0.004675 ReLu 26 1 5 0 2000 11 0.002496 tanh 27 2 3 4 2000 12 0.001760 tanh 47 2 3 4 2000 13 0.001020 ReLu 59 1 8 0 2000 14 0.036207 ReLu 98 1 3 0 2000 15 0.000555 ReLu 63 1 5 0 1...

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    Further reductions did not lead to additional gains. Model Learning Rate Activation Function Batch Size Number of Lay- ers Neurons in Layer 1 Neurons in Layer 2 Epochs 8 0.001074 tanh 44 1 6 0 2000 9 0.001450 tanh 90 1 4 0 2000 10 0.000234 tanh 26 2 5 5 2000 11 0.000204 tanh 38 2 3 9 2000 12 0.059644 ReLu 66 2 7 9 2000 13 0.010095 ReLu 38 1 6 0 2000 14 0....

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    3 WHOLE PERIOD EV ALUATIONS10 Figure 3.2: Duration from the different portfolios between July 2014 and February

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    3.2 Europe Figure 3.3: Performance from the different models and the benchmark between December 2014 and February

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    4 PERIODIC EV ALUATION - U.S.11 Figure 3.4: Duration from the different portfolios in Europe between December 2014 and February

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    Table 4.1: Results for the different models in the period between July 2014 and February

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    Ω MDD Rank

    Model Ret. Ω MDD Rank. Ω Rank. MDD Sum Rank. Rank. P1 B27 0.78 0.95 -7.21 2 2 4 1 N28 0.77 0.93 -7.17 3 1 4 1 B31 1.36 1.06 -7.37 1 3 4 1 Bench. 0.98 - -4.92 - - - - 4 PERIODIC EV ALUATION - U.S.12 Figure 4.1: Performance of the different portfolios between July 2014 and February

    2014

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    Figure 4.2: Duration of the different portfolios between July 2014 and February

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    4 PERIODIC EV ALUATION - U.S.13 Table 4.2: Results for the different models in the period between February 2018 and July

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    Figure 4.3: Performance of the different portfolios between February 2018 and July

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    4 PERIODIC EV ALUATION - U.S.14 Figure 4.4: Duration of the different portfolios between February 2018 and July

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    Table 4.3: Results for the different models in the period between July 2021 and November

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    Ω MDD Rank

    Model Ret. Ω MDD Rank. Ω Rank. MDD Sum Rank. Rank. P3 B27 -6.48 1.43 -9.51 3 3 6 3 N28 -5.96 1.58 -8.73 1 1 2 1 B31 -6.43 1.49 -9.32 2 2 4 2 Bench. -8.02 - -11.50 - - - - 4 PERIODIC EV ALUATION - U.S.15 Figure 4.5: Performance of the different portfolios between July 2021 and November

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    Figure 4.6: Duration of the different portfolios between July 2021 and November

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    4 PERIODIC EV ALUATION - U.S.16 Table 4.4: Results for the different models in the period between November 2022 and February

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    Figure 4.7: Performance of the different portfolios between November 2022 and February

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    5 PERIODIC EV ALUATION - EUROPE17 Figure 4.8: Duration of the different portfolios between November 2022 and February

    2022

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    Table 5.1: Results for the different models in the period between December 2014 and September

    2014

  44. [44]

    Ω MDD Rank

    Model Ret. Ω MDD Rank. Ω Rank. MDD Sum Rank. Rank. P1 N16 2.26 1.19 -7.60 1 3 4 2 E18 1.64 0.93 -5.49 3 2 5 3 E27 1.85 1.04 -5.09 2 1 3 1 Bench. 1.79 - -5.45 - - - - 5 PERIODIC EV ALUATION - EUROPE18 Figure 5.1: Performance of the different portfolios between December 2014 and September

    2014

  45. [45]

    Figure 5.2: Duration of the different portfolios between December 2014 and September

    2014

  46. [46]

    5 PERIODIC EV ALUATION - EUROPE19 Table 5.2: Results for the different models in the period between September 2019 and November

    2019

  47. [47]

    Figure 5.3: Performance of the different portfolios between September 2019 and November

    2019

  48. [48]

    5 PERIODIC EV ALUATION - EUROPE20 Figure 5.4: Duration of the different portfolios between September 2019 and November

    2019

  49. [49]

    Table 5.3: Results for the different models in the period between December 2021 and October

    2021

  50. [50]

    Ω MDD Rank

    Model Ret. Ω MDD Rank. Ω Rank. MDD Sum Rank. Rank. P3 N16 -3.69 1.89 -7.57 1 3 4 1 E18 -3.14 1.88 -7.47 2 2 4 1 E27 -2.50 1.78 -6.53 3 1 4 1 Bench. -6.55 - -12.52 - - - - 5 PERIODIC EV ALUATION - EUROPE21 Figure 5.5: Performance of the different portfolios between December 2021 and October

    2021

  51. [51]

    Figure 5.6: Duration of the different portfolios between December 2021 and October

    2021

  52. [52]

    5 PERIODIC EV ALUATION - EUROPE22 Table 5.4: Results for the different models in the period between October 2023 and Febru- ary

    2023

  53. [53]

    Figure 5.7: Performance of the different portfolios between October 2023 and February

    2023

  54. [54]

    5 PERIODIC EV ALUATION - EUROPE23 Figure 5.8: Duration of the different portfolios between October 2023 and February 2025

    2023