Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications

Marcos Escobar-Anel (), Sebastian Ferrando, Fuyu Li and Ke Xu
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Marcos Escobar-Anel: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
Sebastian Ferrando: Department of Mathematics, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada
Fuyu Li: Department of Economics, University of Victoria, Victoria, BC V8P 5C2, Canada
Ke Xu: Department of Economics, University of Victoria, Victoria, BC V8P 5C2, Canada
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

Econometrics, 2025, vol. 13, issue 1, 1-17

Abstract: This paper revisits the topic of time-scale parameterizations of the Heston–Nandi GARCH (1,1) model to create a new, theoretically valid setting compatible with real financial data. We first estimate parameters using three US market indices and six frequencies to let data reveal the correct, data-implied, time-scale parameterizations. We compared the data-implied parametrization to two popular candidates in the literature, demonstrating structurally different continuous-time limits, i.e., the data favor fractional Brownian motion (fBM)—instead of the standard Brownian motion (BM)-based parametrization. We then propose a theoretically flexible time-scale parameterization compatible with this fBM behavior. In this context, a fractional derivative analysis of our empirically based parametrization is performed, confirming an anomalous diffusion in the continuous-time limit. Such a finding is yet another endorsement of the recent and popular stylized fact known as rough volatility.

Keywords: Affine GARCH; maximum likelihood estimation; time-scale parameterization; rough volatility (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2025
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