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Stationarity-based specification tests for diffusions when the process is nonstationary

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  • Aït-Sahalia, Yacine
  • Park, Joon Y.

Abstract

We analyze in this paper the asymptotic behavior of the specification test of Aït-Sahalia (1996) for the stationary density of a diffusion process, but when the diffusion is not stationary. We consider integrated and explosive processes, as well as nearly integrated ones in the spirit of the local to unity analysis in classical unit root theory. We find that the behavior of the test predicted by the asymptotic distribution under an integrated process provides a better approximation to the small sample distribution of the test than that predicted by the asymptotic distribution under strict stationarity.

Suggested Citation

  • Aït-Sahalia, Yacine & Park, Joon Y., 2012. "Stationarity-based specification tests for diffusions when the process is nonstationary," Journal of Econometrics, Elsevier, vol. 169(2), pages 279-292.
    • Handle: RePEc:eee:econom:v:169:y:2012:i:2:p:279-292
    DOI: 10.1016/j.jeconom.2012.01.030
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    References listed on IDEAS

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    Cited by:

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    3. Li, Yingying & Liu, Guangying & Zhang, Zhiyuan, 2022. "Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps," Journal of Econometrics, Elsevier, vol. 229(2), pages 422-451.
    4. Jeong, Minsoo, 2022. "Modelling persistent stationary processes in continuous time," Economic Modelling, Elsevier, vol. 109(C).
    5. Zu, Yang & Boswijk, H. Peter, 2017. "Consistent nonparametric specification tests for stochastic volatility models based on the return distribution," Journal of Empirical Finance, Elsevier, vol. 41(C), pages 53-75.
    6. Zu, Y., 2015. "Consistent nonparametric specification tests for stochastic volatility models based on the return distribution," Working Papers 15/02, Department of Economics, City University London.
    7. Choi, Yongok & Jacewitz, Stefan & Park, Joon Y., 2016. "A reexamination of stock return predictability," Journal of Econometrics, Elsevier, vol. 192(1), pages 168-189.
    8. Bu, Ruijun & Kim, Jihyun & Wang, Bin, 2023. "Uniform and Lp convergences for nonparametric continuous time regressions with semiparametric applications," Journal of Econometrics, Elsevier, vol. 235(2), pages 1934-1954.
    9. Zu, Yang, 2015. "Nonparametric specification tests for stochastic volatility models based on volatility density," Journal of Econometrics, Elsevier, vol. 187(1), pages 323-344.

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