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The Bickel-Rosenblatt test for diffusion processes

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  • Lee, Sangyeol

Abstract

In this paper, we consider the Bickel-Rosenblatt test for a class of diffusion processes that covers the Ornstein-Uhlenbeck process. Using the discrete sampling scheme, we calculate residuals and construct the residual based Bickel-Rosenblatt test. We show that the test statistic is asymptotically normal under regularity conditions. The result is applicable to the test for the existence of jumps in diffusion models.

Suggested Citation

  • Lee, Sangyeol, 2006. "The Bickel-Rosenblatt test for diffusion processes," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1494-1502, August.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:14:p:1494-1502
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    References listed on IDEAS

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    1. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    2. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796, December.
    3. Koichi Maekawa & Sangyeol & Lee, 2004. "The Cusum Test for Parameter Change in Regression with ARCH Errors," Econometric Society 2004 Far Eastern Meetings 606, Econometric Society.
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    Cited by:

    1. Sangyeol Lee & Hiroki Masuda, 2010. "Jarque–Bera normality test for the driving Lévy process of a discretely observed univariate SDE," Statistical Inference for Stochastic Processes, Springer, vol. 13(2), pages 147-161, June.

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