IDEAS home Printed from https://ideas.repec.org/p/aah/create/2009-39.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: ftp://ftp.econ.au.dk/creates/rp/09/rp09_39.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Robert R. Bliss, 1997. "Movements in the term structure of interest rates," Economic Review, Federal Reserve Bank of Atlanta, issue Q 4, pages 16-33.
    2. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    3. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    4. Bowsher, Clive G. & Meeks, Roland, 2008. "The Dynamics of Economic Functions: Modeling and Forecasting the Yield Curve," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1419-1437.
    5. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    6. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2012. "A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1014-1024, November.
    7. Connor, Gregory & Korajczyk, Robert A, 1993. " A Test for the Number of Factors in an Approximate Factor Model," Journal of Finance, American Finance Association, vol. 48(4), pages 1263-1291, September.
    8. Gregory, Allan W & Head, Allen C & Raynauld, Jacques, 1997. "Measuring World Business Cycles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 677-701, August.
    9. de Jong, Frank, 2000. "Time Series and Cross-Section Information in Affine Term-Structure Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 300-314, July.
    10. Diebold, Francis X. & Rudebusch, Glenn D. & Borag[caron]an Aruoba, S., 2006. "The macroeconomy and the yield curve: a dynamic latent factor approach," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 309-338.
    11. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    12. Watson, Mark W. & Engle, Robert F., 1983. "Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models," Journal of Econometrics, Elsevier, vol. 23(3), pages 385-400, December.
    13. Thomas J. Sargent & Christopher A. Sims, 1977. "Business cycle modeling without pretending to have too much a priori economic theory," Working Papers 55, Federal Reserve Bank of Minneapolis.
    14. Reis, Ricardo & Watson, Mark W, 2007. "Relative Goods’ Prices and Pure Inflation," CEPR Discussion Papers 6593, C.E.P.R. Discussion Papers.
    15. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, June.
    16. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    17. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    18. Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-126, February.
    19. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826 Elsevier.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Fama-Bliss data set; Kalman filter; Maximum likelihood; Yield curve;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aah:create:2009-39. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://www.econ.au.dk/afn/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.