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GARCH quasi-likelihood ratios for SV model and the diffusion limit

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  • Song, Xinyu
  • Wang, Yazhen

Abstract

There is a widely known intriguing phenomenon that discrete-time GARCH and stochastic volatility (SV) models share the same continuous-time diffusion model as their weak convergence limit, but statistically, the GARCH model is not asymptotically equivalent to the SV or diffusion model. This paper investigates GARCH-type quasi-likelihood ratios for the SV and diffusion models whose own likelihoods are analytically intractable. We show that the two quasi-likelihood ratios for the SV and diffusion models asymptotically have the same closed-form expression that is different from the limiting likelihood ratio of the GARCH model.

Suggested Citation

  • Song, Xinyu & Wang, Yazhen, 2020. "GARCH quasi-likelihood ratios for SV model and the diffusion limit," Statistics & Probability Letters, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:stapro:v:165:y:2020:i:c:s0167715220301206
    DOI: 10.1016/j.spl.2020.108817
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    References listed on IDEAS

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