Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications
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-im...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
|
| Series: | Econometrics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2225-1146/13/1/6 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850203782879641600 |
|---|---|
| author | Marcos Escobar-Anel Sebastian Ferrando Fuyu Li Ke Xu |
| author_facet | Marcos Escobar-Anel Sebastian Ferrando Fuyu Li Ke Xu |
| author_sort | Marcos Escobar-Anel |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-204c5dd4a5ea4cb280986ff34660eebf |
| institution | OA Journals |
| issn | 2225-1146 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Econometrics |
| spelling | doaj-art-204c5dd4a5ea4cb280986ff34660eebf2025-08-20T02:11:25ZengMDPI AGEconometrics2225-11462025-02-01131610.3390/econometrics13010006Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness ImplicationsMarcos Escobar-Anel0Sebastian Ferrando1Fuyu Li2Ke Xu3Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, CanadaDepartment of Mathematics, Toronto Metropolitan University, Toronto, ON M5B 2K3, CanadaDepartment of Economics, University of Victoria, Victoria, BC V8P 5C2, CanadaDepartment of Economics, University of Victoria, Victoria, BC V8P 5C2, CanadaThis 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.https://www.mdpi.com/2225-1146/13/1/6Affine GARCHmaximum likelihood estimationtime-scale parameterizationrough volatility |
| spellingShingle | Marcos Escobar-Anel Sebastian Ferrando Fuyu Li Ke Xu Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications Econometrics Affine GARCH maximum likelihood estimation time-scale parameterization rough volatility |
| title | Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications |
| title_full | Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications |
| title_fullStr | Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications |
| title_full_unstemmed | Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications |
| title_short | Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications |
| title_sort | data based parametrization for affine garch models across multiple time scales roughness implications |
| topic | Affine GARCH maximum likelihood estimation time-scale parameterization rough volatility |
| url | https://www.mdpi.com/2225-1146/13/1/6 |
| work_keys_str_mv | AT marcosescobaranel databasedparametrizationforaffinegarchmodelsacrossmultipletimescalesroughnessimplications AT sebastianferrando databasedparametrizationforaffinegarchmodelsacrossmultipletimescalesroughnessimplications AT fuyuli databasedparametrizationforaffinegarchmodelsacrossmultipletimescalesroughnessimplications AT kexu databasedparametrizationforaffinegarchmodelsacrossmultipletimescalesroughnessimplications |