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Nonparametric density estimation and tests of continuous time interest rate models

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  • Matthew Pritsker

Abstract

Nonparametric kernel density estimation has recently been used to estimate and test short-term interest rate models, but inference has been based on asymptotics. We derive finite sample properties of kernel density estimates of the ergodic distribution of the short-rate when it follows a continuous time AR(1) as in Vasicek. We find that the asymptotic distribution substantially understates finite sample bias, variance, and correlation. Also, estimator quality and bandwidth choice depend strongly on the persistence of the interest rate process and on the span of the data, but not on sampling frequency. We also examine the size and power of one of Ait-Sahalia's nonparametric tests of continuous time interest rate models. The test rejects too often. This is probably because the quality of the nonparametric density estimate depends on persistence, but the asymptotic distribution of the test does not. After critical values are adjusted for size, the test has low power in distinguishing between the Vasicek and Cox-Ingersoll-Ross models relative to a conditional moment-based specification test.

Suggested Citation

  • Matthew Pritsker, 1997. "Nonparametric density estimation and tests of continuous time interest rate models," Finance and Economics Discussion Series 1997-26, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:1997-26
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    References listed on IDEAS

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    1. 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.
    2. Broze, Laurence & Scaillet, Olivier & Zakoian, Jean-Michel, 1995. "Testing for continuous-time models of the short-term interest rate," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 199-223, September.
    3. Ball, Clifford A. & Torous, Walter N., 1996. "Unit roots and the estimation of interest rate dynamics," Journal of Empirical Finance, Elsevier, vol. 3(2), pages 215-238, June.
    4. 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..
    5. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    6. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    7. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    8. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    9. Pagan, A.R. & Hall, A.D. & Martin, V., 1995. "Modelling the Term Structure," Papers 284, Australian National University - Department of Economics.
    10. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    11. Wand, M. P., 1992. "Finite sample performance of density estimators under moving average dependence," Statistics & Probability Letters, Elsevier, vol. 13(2), pages 109-115, January.
    12. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
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    Cited by:

    1. Filippo Altissimo & Valentina Corradi, 2000. "Strong Rules for Detecting the Number of Breaks in a Time Series," Econometric Society World Congress 2000 Contributed Papers 0574, Econometric Society.
    2. Stanislav Anatolyev & Sergey Korepanov, 2003. "The term structure of Russian interest rates," Applied Economics Letters, Taylor & Francis Journals, vol. 10(13), pages 867-870.

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    Keywords

    Interest rates ; Time-series analysis;

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