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

Xinyu Song and Yazhen Wang

Statistics & Probability Letters, 2020, vol. 165, issue C

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.

Keywords: Approximating process; Financial modeling; Likelihood process; Stochastic differential equation; Stochastic volatility (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108817

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