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A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions

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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.

Suggested Citation

  • 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.
    • Handle: RePEc:cwl:cwldpp:1522
    Note: CFP 1205.
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    More about this item

    Keywords

    Diffusion; Drift; Local time; Parametric estimation; Semimartingale; Stochastic differential equation;
    All these keywords.

    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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