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A Model Specification Test for Nonlinear Stochastic Diffusions with Delay

Author

Listed:
  • Zongwu Cai

    (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA)

  • Hongwei Mei

    (Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA)

  • Rui Wang

    (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA)

Abstract

The paper investigates model specification problems for nonlinear stochastic differential equations with delay (SDDE). Compared to the model specification for conventional stochastic diffusions without delay, the observed sequence does not admit a Markovian structure so that the classical testing procedures fail. To overcome this difficulty, we propose a moment estimator from the ergodicity of SDDEs and its asymptotic properties are established. Based on the proposed moment estimator, a testing procedure is derived for our model specification testing problems. Particularly, the limiting distributions of the proposed test statistic are derived under null hypotheses and the test power is obtained under some specific alternative hypotheses. Finally, a Monte Carlo simulation is conducted to illustrate the finite sample performance of the proposed test.

Suggested Citation

  • Zongwu Cai & Hongwei Mei & Rui Wang, 2023. "A Model Specification Test for Nonlinear Stochastic Diffusions with Delay," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202301, University of Kansas, Department of Economics, revised Jan 2023.
    • Handle: RePEc:kan:wpaper:202301
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    File URL: https://kuwpaper.ku.edu/2023Papers/202301.pdf
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    References listed on IDEAS

    as
    1. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    2. Jakub Steiner & Colin Stewart & Filip Matějka, 2017. "Rational Inattention Dynamics: Inertia and Delay in Decision‐Making," Econometrica, Econometric Society, vol. 85, pages 521-553, March.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    6. Aït-Sahalia, Yacine & Fan, Jianqing & Peng, Heng, 2009. "Nonparametric Transition-Based Tests for Jump Diffusions," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1102-1116.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Model specification test; Stochastic differential equation with delay; Moment estimator; Ergodicity; Invariant measure; Non-Markovian property.;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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