Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes
AbstractThe asymptotic distributions of the least squares estimator of the mean reversion parameter (κ) are developed in a general class of diffusion models under three sampling schemes, namely, longspan, in-fill and the combination of long-span and in-fill. The models have an affine structure in the drift function, but allow for nonlinearity in the diffusion function. The limiting distributions are quite different under the alternative sampling schemes. In particular, the in-fill limiting distribution is non-standard and depends on the initial condition and the time span whereas the other two are Gaussian. Moreover, while the other two distributions are discontinuous at κ = 0, the in-fill distribution is continuous in κ. This property provides an answer to the Bayesian criticism to the unit root asymptotics. Monte Carlo simulations suggest that the in-fill asymptotic distribution provides a more accurate approximation to the finite sample distribution than the other two distributions in empirically realistic settings. The empirical application using the U.S. Federal fund rates highlights the difference in statistical inference based on the alternative asymptotic distributions and suggests strong evidence of a unit root in the data.
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Bibliographic InfoPaper provided by Singapore Management University, School of Economics in its series Working Papers with number 20-2010.
Length: 40 pages
Date of creation: Jan 2010
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Other versions of this item:
- Qiankun Zhou & Jun Yu, 2012. "Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes," Working Papers 11-2012, Singapore Management University, School of Economics.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-11-27 (All new papers)
- NEP-ECM-2010-11-27 (Econometrics)
- NEP-ETS-2010-11-27 (Econometric Time Series)
- NEP-SEA-2010-11-27 (South East Asia)
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- David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007.
"Unit root testing in practice: dealing with uncertainty over the trend and initial condition,"
07/03, University of Nottingham, Granger Centre for Time Series Econometrics.
- Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(03), pages 587-636, June.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Ole E. Barndorff-Nielsen & Shephard, 2002.
"Econometric analysis of realized volatility and its use in estimating stochastic volatility models,"
Journal of the Royal Statistical Society Series B,
Royal Statistical Society, vol. 64(2), pages 253-280.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
- Peter C.B. Phillips & Tassos Magdalinos, 2004.
"Limit Theory for Moderate Deviations from a Unit Root,"
Cowles Foundation Discussion Papers
1471, Cowles Foundation for Research in Economics, Yale University.
- Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
- Chan, K C, et al, 1992.
" An Empirical Comparison of Alternative Models of the Short-Term Interest Rate,"
Journal of Finance,
American Finance Association, vol. 47(3), pages 1209-27, July.
- Tom Doan, . "RATS programs to replicate CKLS(1992) estimation of interest rate models," Statistical Software Components RTZ00035, Boston College Department of Economics.
- Bandi, Federico M. & Phillips, Peter C.B., 2007.
"A simple approach to the parametric estimation of potentially nonstationary diffusions,"
Journal of Econometrics,
Elsevier, vol. 137(2), pages 354-395, April.
- Federico M. Bandi & Peter C.B. Phillips, 2005. "A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions," Cowles Foundation Discussion Papers 1522, Cowles Foundation for Research in Economics, Yale University.
- Peter C. B. Phillips & Chirok Han, 2006.
"Gaussian Inference in AR(1) Time Series with or without a Unit Root,"
Cowles Foundation Discussion Papers
1546, Cowles Foundation for Research in Economics, Yale University.
- Phillips, Peter C.B. & Han, Chirok, 2008. "Gaussian Inference In Ar(1) Time Series With Or Without A Unit Root," Econometric Theory, Cambridge University Press, vol. 24(03), pages 631-650, June.
- Phillips, P C B, 1987.
"Time Series Regression with a Unit Root,"
Econometric Society, vol. 55(2), pages 277-301, March.
- Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- David A. Chapman & Neil D. Pearson, 1998.
"Is the Short Rate Drift Actually Nonlinear?,"
- Sims, Christopher A & Uhlig, Harald, 1991.
"Understanding Unit Rooters: A Helicopter Tour,"
Econometric Society, vol. 59(6), pages 1591-99, November.
- Christopher A. Sims & Harald Uhlig, 1988. "Understanding unit rooters: a helicopter tour," Discussion Paper / Institute for Empirical Macroeconomics 4, Federal Reserve Bank of Minneapolis.
- Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
- Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-87.
- Haldrup, Niels & Hylleberg, Svend, 1995. "A note on the distribution of the least squares estimator of a random walk with drift: Some analytical evidence," Economics Letters, Elsevier, vol. 48(3-4), pages 221-228, June.
- Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
- Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, 07.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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