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A simple approach to the parametric estimation of potentially nonstationary diffusions

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  • Bandi, Federico M.
  • Phillips, Peter C.B.

Abstract

A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic differential equations. We specify a parametric class of diffusions and estimate the parameters of interest by minimizing criteria based on the integrated squared difference between kernel estimates of the drift and diffusion functions and their parametric counterparts. The procedure does not require simulations or approximations to the true transition density and has the simplicity of standard nonlinear least-squares methods in discrete-time. A complete asymptotic theory for the parametric estimates is developed. The limit theory relies on infill and long span asymptotics and is robust to deviations from stationarity, requiring only recurrence.
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  • 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.
    • Handle: RePEc:eee:econom:v:137:y:2007:i:2:p:354-395
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    Cited by:

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    5. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
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    7. Chaohua Dong & Jiti Gao, 2013. "Orthogonal Expansion of Levy Process Functionals: Theory and Practice," Monash Econometrics and Business Statistics Working Papers 3/13, Monash University, Department of Econometrics and Business Statistics.
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    9. Bu, Ruijun & Hadri, Kaddour & Kristensen, Dennis, 2021. "Diffusion copulas: Identification and estimation," Journal of Econometrics, Elsevier, vol. 221(2), pages 616-643.
    10. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.
    11. Phillips, Peter C.B. & Yu, Jun, 2009. "A two-stage realized volatility approach to estimation of diffusion processes with discrete data," Journal of Econometrics, Elsevier, vol. 150(2), pages 139-150, June.
    12. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
    13. Yu, Jun, 2014. "Econometric Analysis Of Continuous Time Models: A Survey Of Peter Phillips’S Work And Some New Results," Econometric Theory, Cambridge University Press, vol. 30(4), pages 737-774, August.
    14. Song, Zhaogang, 2011. "A martingale approach for testing diffusion models based on infinitesimal operator," Journal of Econometrics, Elsevier, vol. 162(2), pages 189-212, June.
    15. Chaohua Dong & Jiti Gao, 2011. "Expansion of Brownian Motion Functionals and Its Application in Econometric Estimation," Monash Econometrics and Business Statistics Working Papers 19/11, Monash University, Department of Econometrics and Business Statistics.
    16. Jun Yu, 2009. "Econometric Analysis of Continuous Time Models : A Survey of Peter Phillips’ Work and Some New Results," Microeconomics Working Papers 23046, East Asian Bureau of Economic Research.
    17. Qiankun Zhou & Jun Yu, 2010. "Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes," Working Papers 20-2010, Singapore Management University, School of Economics.
    18. Becheri, I.G., 2012. "Limiting experiments for panel-data and jump-diffusion models," Other publications TiSEM 7e53f6cf-fab1-4f86-9e5d-b, Tilburg University, School of Economics and Management.
    19. Chaohua Dong & Jiti Gao, 2012. "Expansion of Lévy Process Functionals and Its Application in Statistical Estimation," Monash Econometrics and Business Statistics Working Papers 2/12, Monash University, Department of Econometrics and Business Statistics.
    20. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.
    21. Aman Ullah & Yong Bao & Yun Wang, 2014. "Exact Distribution of the Mean Reversion Estimator in the Ornstein-Uhlenbeck Process," Working Papers 201413, University of California at Riverside, Department of Economics.
    22. Peter C.B. Phillips & Jun Yu, 2005. "A Two-Stage Realized Volatility Approach to the Estimation for Diffusion Processes from Discrete Observations," Cowles Foundation Discussion Papers 1523, Cowles Foundation for Research in Economics, Yale University.
    23. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 390-455.
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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