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

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Author Info

  • 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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-39.

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Length: 38
Date of creation: 08 Sep 2009
Date of revision:
Handle: RePEc:aah:create:2009-39

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Web page: http://www.econ.au.dk/afn/

Related research

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

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References

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  1. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, Econometric Society, vol. 71(1), pages 135-171, January.
  2. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
  3. de Jong, Frank, 2000. "Time Series and Cross-Section Information in Affine Term-Structure Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 18(3), pages 300-314, July.
  4. 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 116-26, February.
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  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 1263-91, September.
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  9. Clive Bowsher & Roland Meeks, 2008. "The Dynamics of Economic Functions: Modelling and Forecasting the Yield Curve," OFRC Working Papers Series 2008fe24, Oxford Financial Research Centre.
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  12. 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.
  13. Jens H.E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007. "The affine arbitrage-free class of Nelson-Siegel term structure models," Working Paper Series 2007-20, Federal Reserve Bank of San Francisco.
  14. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, Elsevier, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826 Elsevier.
  15. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(2), pages 147-62, April.
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  18. 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.
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