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Specification Analysis of Affine Term Structure Models

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  • Qiang Dai
  • Kenneth J. Singleton

Abstract

In this paper, we explore the features of affine term structure models that are empirically important for explaining the joint distribution of yields on short and long-term interest rate swaps. We begin by showing that the family of N-factor affine models can be classified into N+1 non-nested sub-families of models. For each sub-family, we derive a maximal model with the property that every admissible member of this family is equivalent to or a nested special case of our maximal model. Second, using our classification scheme and maximal models, we show that many of the three-factor models in the literature impose potentially strong over-identifying restrictions on the joint distribution of short- and long-term rates. Third, we compute simulated method-of-moments estimates for several members of one of the four branches of three-factor models, and test the over-identifying restrictions implied by these models. We conclude that many of the extant affine models in the literature fail to describe important features of the distribution of long- and short- term rates. The source of the model misspecification is shown to be overly strong restrictions on the correlations among the state variables. Relaxing these restrictions leads to a model that passes several goodness-of-fit tests over our sample period.

Suggested Citation

  • Qiang Dai & Kenneth J. Singleton, 1998. "Specification Analysis of Affine Term Structure Models," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-083, New York University, Leonard N. Stern School of Business-.
  • Handle: RePEc:fth:nystfi:98-083
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    References listed on IDEAS

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    1. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
    2. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    3. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
    4. Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1998. "The Central Tendency: A Second Factor In Bond Yields," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 62-72, February.
    5. David Backus & Silverio Foresi & Chris Telmer, 1996. "Affine Models of Currency Pricing," NBER Working Papers 5623, National Bureau of Economic Research, Inc.
    6. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    7. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-787, October.
    8. David K. Backus & Stanley E. Zin, 1994. "Reverse Engineering the Yield Curve," NBER Working Papers 4676, National Bureau of Economic Research, Inc.
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