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Smooth Dynamic Factor Analysis with an Application to the U.S. Term Structure of Interest Rates

Author

Listed:
  • Borus Jungbacker

    (Department of Econometrics, VU University Amsterdam)

  • Siem Jan Koopman

    (Department of Econometrics, VU University Amsterdam and Tinbergen Institute)

  • Michel van der Wel

    (Tinbergen Institute + Erasmus School of Economics, ERIM Rotterdam + CREATES, Aarhus University)

Abstract

We consider the dynamic factor model and show how smoothness restrictions can be imposed on the factor loadings. Cubic spline functions are used to introduce smoothness in factor loadings. We develop statistical procedures based on Wald, Lagrange multiplier and likelihood ratio tests for this purpose. A Monte Carlo study is presented to show that our procedures are successful in identifying smooth loading structures from small sample panels. We illustrate the methodology by analyzing the U.S. term structure of interest rates. An empirical study is carried out using a monthly time series panel of unsmoothed Fama-Bliss zero yields for treasuries of different maturities between 1970 and 2009. Dynamic factor models with and without smooth loadings are compared with dynamic models based on Nelson-Siegel and cubic spline yield curves. All models can be regarded as special cases of the dynamic factor model. We carry out statistical hypothesis tests and compare information criteria to verify whether the restrictions imposed by the models are supported by the data. Out-of-sample forecast evidence is also given. Our main conclusion is that smoothness restrictions on loadings of the dynamic factor model for the term structure can be supported by our panel of U.S. interest rates and can lead to more accurate forecasts.

Suggested Citation

  • Borus Jungbacker & Siem Jan Koopman & Michel van der Wel, 2009. "Smooth Dynamic Factor Analysis with an Application to the U.S. Term Structure of Interest Rates," CREATES Research Papers 2009-39, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2009-39
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    2. Caldeira, João F. & Moura, Guilherme V. & Santos, André A.P., 2016. "Bond portfolio optimization using dynamic factor models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 128-158.
    3. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    4. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    5. Sven Otto & Nazarii Salish, 2022. "Approximate Factor Models for Functional Time Series," Papers 2201.02532, arXiv.org, revised Feb 2025.
    6. Ken Nyholm, 2018. "A Rotated Dynamic Nelson†Siegel Model," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 47(1), pages 113-124, February.
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    8. Feng, Pan & Qian, Junhui, 2018. "Forecasting the yield curve using a dynamic natural cubic spline model," Economics Letters, Elsevier, vol. 168(C), pages 73-76.
    9. Konstantinos Bisiotis & Stelios Psarakis & Athanasios N. Yannacopoulos, 2022. "Affine Term Structure Models: Applications in Portfolio Optimization and Change Point Detection," Mathematics, MDPI, vol. 10(21), pages 1-33, November.
    10. Michel van der Wel & Sait R. Ozturk & Dick van Dijk, 2015. "Dynamic Factor Models for the Volatility Surface," CREATES Research Papers 2015-13, Department of Economics and Business Economics, Aarhus University.
    11. Geert Mesters & Victor van der Geest & Catrien Bijleveld, 2014. "Crime, Employment and Social Welfare: an Individual-level Study on Disadvantaged Males," Tinbergen Institute Discussion Papers 14-091/III, Tinbergen Institute.

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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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