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A study of the finite sample properties of EMM, GMM, QMLE, and MLE for a square-root interest rate diffusion model

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Hao Zhou

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Abstract

This paper performs a Monte Carlo study on Efficient Method of Moments (EMM), Generalized Method of Moments (GMM), Quasi-Maximum Likelihood Estimation (QMLE), and Maximum Likelihood Estimation (MLE) for a continuous-time square-root model under two challenging scenarios--high persistence in mean and strong conditional volatility--that are commonly found in estimating the interest rate process. MLE turns out to be the most efficient of the four methods, but its finite sample inference and convergence rate suffer severely from approximating the likelihood function, especially in the scenario of highly persistent mean. QMLE comes second in terms of estimation efficiency, but it is the most reliable in generating inferences. GMM with lag-augmented moments has overall the lowest estimation efficiency, possibly due to the ad hoc choice of moment conditions. EMM shows an accelerated convergence rate in the high volatility scenario, while its overrejection bias in the mean persistence scenario is unacceptably large. Finally, under a stylized alternative model of the US interest rates, the overidentification test of EMM obtains the ultimate power for detecting misspecification, while the GMM J-test is increasingly biased downward in finite samples.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2000-45.

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Date of creation: 2000
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Handle: RePEc:fip:fedgfe:2000-45

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Keywords: Interest rates ; Econometrics;

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References listed on IDEAS
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    Other versions:
  4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
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  11. Bansal, Ravi & Gallant, A. Ronald & Hussey, Robert & Tauchen, George, 1995. "Nonparametric estimation of structural models for high-frequency currency market data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 251-287. [Downloadable!] (restricted)
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    Other versions:
  13. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
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  16. Gallant, A. Ronald & Tauchen, George, 1997. "Reprojecting Partially Observed Systems with Application to Interest Rate Diffusions," Working Papers 97-09, Duke University, Department of Economics.
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  18. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July. [Downloadable!] (restricted)
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  23. repec:bep:sndecm:2:1997:2:35-51 is not listed on IDEAS
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Tim Bollerslev & Hao Zhou, 2001. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Finance and Economics Discussion Series 2001-49, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
    Other versions:
  2. Hao Zhou, 2003. "Itô conditional moment generator and the estimation of short rate processes," Finance and Economics Discussion Series 2003-32, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
    Other versions:
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