IDEAS home Printed from https://ideas.repec.org/p/fip/feddwp/0804.html
   My bibliography  Save this paper

The dynamics of economics functions: modelling and forecasting the yield curve

Author

Listed:
  • Bowsher, Clive G.
  • Meeks, Roland

Abstract

The class of Functional Signal plus Noise (FSN) models is introduced that provides a new, general method for modelling and forecasting time series of economic functions. The underlying, continuous economic function (or "signal") is a natural cubic spline whose dynamic evolution is driven by a cointegrated vector autoregression for the ordinates (or "y-values") at the knots of the spline. The natural cubic spline provides flexible cross-sectional fit and results in a linear, state space model. This FSN model achieves dimension reduction, provides a coherent description of the observed yield curve and its dynamics as the cross-sectional dimension N becomes large, and can feasibly be estimated and used for forecasting when N is large. The integration and cointegration properties of the model are derived. The FSN models are then applied to forecasting 36-dimensional yield curves for US Treasury bonds at the one month ahead horizon. The method consistently outperforms the Diebold and Li (2006) and random walk forecasts on the basis of both mean square forecast error criteria and economically relevant loss functions derived from the realised profits of pairs trading algorithms. The analysis also highlights in a concrete setting the dangers of attempts to infer the relative economic value of model forecasts on the basis of their associated mean square forecast errors.

Suggested Citation

  • Bowsher, Clive G. & Meeks, Roland, 2008. "The dynamics of economics functions: modelling and forecasting the yield curve," Working Papers 0804, Federal Reserve Bank of Dallas.
  • Handle: RePEc:fip:feddwp:0804 Note: Published as: Bowsher, Clive G. and Roland Meeks (2008), "The Dynamics of Economic Functions: Modelling and Forecasting the Yield Curve," Journal of the American Statistical Association 130 (484): 1419-1437.
    as

    Download full text from publisher

    File URL: http://dallasfed.org/assets/documents/research/papers/2008/wp0804.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andrew Jeffrey & Oliver Linton & Thong Nguyen, 2006. "Flexible Term Structure Estimation: Which Method is Preferred?," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(1), pages 99-122, February.
    2. 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.
    3. Philippe C. Besse, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687.
    4. Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, Elsevier.
    5. Clive G. Bowsher, 2004. "Modelling the Dynamics of Cross-Sectional Price Functions: an Econometric Analysis of the Bid and Ask Curves of an Automated Exchange," OFRC Working Papers Series 2004fe19, Oxford Financial Research Centre.
    6. Siem Jan Koopman & Marius Ooms, 2003. "Time Series Modelling of Daily Tax Revenues," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(4), pages 439-469.
    7. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    8. Shea, Gary S, 1992. "Benchmarking the Expectations Hypothesis of the Interest-Rate Term Structure: An Analysis of Cointegration Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 347-366, July.
    9. Jean Boivin & Serena Ng, 2005. "Understanding and Comparing Factor-Based Forecasts," International Journal of Central Banking, International Journal of Central Banking, vol. 1(3), December.
    10. 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.
    11. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-830, June.
    12. DeRossi, G. & Harvey, A., 2006. "Time-Varying Quantiles," Cambridge Working Papers in Economics 0649, Faculty of Economics, University of Cambridge.
    13. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May.
    14. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    15. Clements, M.P. & Hendry, D., 1992. "On the Limitations of Comparing Mean Square Forecast Errors," Economics Series Working Papers 99138, University of Oxford, Department of Economics.
    16. De Pooter, Michiel & Ravazzolo, Francesco & van Dijk, Dick, 2006. "Predicting the term structure of interest rates incorporating parameter uncertainty, model uncertainty and macroeconomic information," MPRA Paper 2512, University Library of Munich, Germany, revised 03 Mar 2007.
    17. Pagan, A.R. & Hall, A.D. & Martin, V., 1995. "Modelling the Term Structure," Papers 284, Australian National University - Department of Economics.
    18. Mark Fisher & Douglas Nychka & David Zervos, 1995. "Fitting the term structure of interest rates with smoothing splines," Finance and Economics Discussion Series 95-1, Board of Governors of the Federal Reserve System (U.S.).
    19. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    20. Zellner, A., 1992. "Statistics, Science and Public Policy," Papers 92-21, California Irvine - School of Social Sciences.
    21. Clive G. Bowsher & Roland Meeks, 2006. "The Impossibility of Stationary Yield Spreads and I(1) Yields under the Expectations Theory of the Term Structure," Economics Papers 2006-W05, Economics Group, Nuffield College, University of Oxford.
    22. Daniel F. Waggoner, 1997. "Spline methods for extracting interest rate curves from coupon bond prices," FRB Atlanta Working Paper 97-10, Federal Reserve Bank of Atlanta.
    23. Tao Wu & Glenn Rudebusch, 2003. "Macroeconomics and the Yield Curve," Computing in Economics and Finance 2003 206, Society for Computational Economics.
    24. Brian P. Sack, 2000. "Using Treasury STRIPS to measure the yield curve," Finance and Economics Discussion Series 2000-42, Board of Governors of the Federal Reserve System (U.S.).
    25. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    26. Fama, Eugene F & Bliss, Robert R, 1987. "The Information in Long-Maturity Forward Rates," American Economic Review, American Economic Association, vol. 77(4), pages 680-692, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hendry, David F. & Martinez, Andrew B., 2017. "Evaluating multi-step system forecasts with relatively few forecast-error observations," International Journal of Forecasting, Elsevier, vol. 33(2), pages 359-372.
    2. Vicente, José & Tabak, Benjamin M., 2008. "Forecasting bond yields in the Brazilian fixed income market," International Journal of Forecasting, Elsevier, vol. 24(3), pages 490-497.
    3. 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.
    4. Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2009. "An arbitrage-free generalized Nelson--Siegel term structure model," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 33-64, November.
    5. Gregory R. Duffee, 2012. "Forecasting interest rates," Economics Working Paper Archive 599, The Johns Hopkins University,Department of Economics.
    6. Tabak, B.M. & Sollaci, A.B. & Gomes, G.M. & Cajueiro, D.O., 2012. "Forecasting the yield curve for the Euro region," Economics Letters, Elsevier, vol. 117(2), pages 513-516.
    7. Dick Dijk & Siem Jan Koopman & Michel Wel & Jonathan H. Wright, 2014. "Forecasting interest rates with shifting endpoints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 693-712, August.
    8. Wolfgang Karl Härdle,Piotr Majer & Melanie Schienle, 2012. "Yield Curve Modeling and Forecasting using Semiparametric Factor Dynamics," SFB 649 Discussion Papers SFB649DP2012-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Ito, Ryoko, 2013. "Modeling Dynamic Diurnal Patterns in High-Frequency Financial Data," Cambridge Working Papers in Economics 1315, Faculty of Economics, University of Cambridge.
    10. Koopman, Siem Jan & van der Wel, Michel, 2013. "Forecasting the US term structure of interest rates using a macroeconomic smooth dynamic factor model," International Journal of Forecasting, Elsevier, vol. 29(4), pages 676-694.
    11. Borus Jungbacker & Siem Jan Koopman & Michel van der Wel, 0000. "Dynamic Factor Models with Smooth Loadings for Analyzing the Term Structure of Interest Rates," Tinbergen Institute Discussion Papers 09-041/4, Tinbergen Institute, revised 17 Sep 2010.
    12. Bekker, Paul A., 2017. "Interpretable Parsimonious Arbitrage-free Modeling of the Yield Curve," Research Report 17009-EEF, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    13. Joao Frois Caldeira & Guilherme Valle Moura & Marcelo Savino Portugal, 2011. "Efficient Interest Ratecurve Estimation And Forecasting In Brazil," Anais do XXXVII Encontro Nacional de Economia [Proceedings of the 37th Brazilian Economics Meeting] 133, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
    14. Ito, R., 2016. "Spline-DCS for Forecasting Trade Volume in High-Frequency Finance," Cambridge Working Papers in Economics 1606, Faculty of Economics, University of Cambridge.
    15. Duffee, Gregory, 2013. "Forecasting Interest Rates," Handbook of Economic Forecasting, Elsevier.
    16. Caio Almeida & Axel Simonsen & José Vicente, 2012. "Forecasting Bond Yields with Segmented Term Structure Models," Working Papers Series 288, Central Bank of Brazil, Research Department.

    More about this item

    Keywords

    Time-series analysis; Forecasting; Mathematical models; Macroeconomics - Econometric models;

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:fip:feddwp:0804. 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: (Amy Chapman). General contact details of provider: http://edirc.repec.org/data/frbdaus.html .

    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.