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Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach

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  • Chen, Bin
  • Song, Zhaogang

Abstract

We develop a nonparametric test to check whether a process can be represented by a stochastic differential equation driven only by a Brownian motion. Our testing procedure utilizes the infinitesimal operator-based martingale characterization combined with a generalized spectral approach. Such a testing procedure is feasible and convenient because the infinitesimal operator of the diffusion process has a closed-form expression. The proposed test is applicable to both univariate and multivariate processes and has an N(0,1) limit distribution under the diffusion hypothesis. Simulation and empirical studies show that the proposed test has reasonable performance in small samples.

Suggested Citation

  • Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    • Handle: RePEc:eee:econom:v:173:y:2013:i:1:p:83-107
    DOI: 10.1016/j.jeconom.2012.10.001
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    More about this item

    Keywords

    Diffusion; Infinitesimal operator; Martingale; Nonparametric;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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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