On the relevance of realized quarticity for exchange rate volatility forecasts

Morten Risstad; Mathias Holand; Morten Risstad; Mathias Holand

doi:10.3934/DSFE.2024021

Data Science in Finance and Economics

2024, Volume 4, Issue 4: 514-530. doi: 10.3934/DSFE.2024021

Previous Article Next Article

Research article Special Issues

On the relevance of realized quarticity for exchange rate volatility forecasts

Morten Risstad ^,,
Mathias Holand

Norwegian University of Science and Technology, Dept. of Industrial Economics and Technology Management, Norway

Received: 21 April 2024 Revised: 15 September 2024 Accepted: 28 October 2024 Published: 30 October 2024
JEL Codes: F31, C58, D53, G17

High-frequency tick data have proved helpful for forecasting volatility across asset classes. In the finite samples typically faced by practitioners, however, noise inherent in tick-level prices creates inaccuracies in model parameter estimates and resulting forecasts. A remedy proposed to alleviate these measurement errors is to include higher-order moments, more specifically the realized quarticity, in volatility prediction models. In this paper, we investigate the relevance of this approach in foreign exchange markets, as represented by EURUSD and USDJPY data from 2010 to 2022. Using well-established realized volatility models, we find that including realized quarticity leads to higher precision in daily, weekly, and monthly out-of-sample forecasts. These results are robust across estimation windows, evaluation metrics, and model specifications.
- foreign exchange,
- volatility,
- high-frequency data,
- realized quarticity,
- multi-period forecasts
Citation: Morten Risstad, Mathias Holand. On the relevance of realized quarticity for exchange rate volatility forecasts[J]. Data Science in Finance and Economics, 2024, 4(4): 514-530. doi: 10.3934/DSFE.2024021

Related Papers:

Abstract

High-frequency tick data have proved helpful for forecasting volatility across asset classes. In the finite samples typically faced by practitioners, however, noise inherent in tick-level prices creates inaccuracies in model parameter estimates and resulting forecasts. A remedy proposed to alleviate these measurement errors is to include higher-order moments, more specifically the realized quarticity, in volatility prediction models. In this paper, we investigate the relevance of this approach in foreign exchange markets, as represented by EURUSD and USDJPY data from 2010 to 2022. Using well-established realized volatility models, we find that including realized quarticity leads to higher precision in daily, weekly, and monthly out-of-sample forecasts. These results are robust across estimation windows, evaluation metrics, and model specifications.

References

[1]	Andersen TG, Bollerslev T (1998) Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. Int Econ Rev 9: 885–905. https://doi.org/10.2307/2527343 doi: 10.2307/2527343
[2]	Andersen TG, Bollerslev T, Diebold FX (2007) Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility. Rev Econ Stat 4: 701–720. https://doi.org/10.1162/rest.89.4.701 doi: 10.1162/rest.89.4.701
[3]	Andersen TG, Bollerslev T, Diebold FX, et al. (2003) Modeling and forecasting realized volatility. Econometrica 2: 579–625. https://doi.org/10.1111/1468-0262.00418 doi: 10.1111/1468-0262.00418
[4]	Andersen TG, Bollerslev T, Christoffersen PF, et al. (2013) Financial risk measurement for financial risk management. Handbook Econ Financ 2: 1127–1220. https://doi.org/10.1016/B978-0-44-459406-8.00017-2 doi: 10.1016/B978-0-44-459406-8.00017-2
[5]	Andersen TG, Li Y, Todorov V, et al. (2023) Volatility measurement with pockets of extreme return persistence. J Econometrics 2: 105048. https://doi.org/10.1016/j.jeconom.2020.11.005
[6]	Audrino F, Chassot J (2024) HARd to Beat: The Overlooked Impact of Rolling Windows in the Era of Machine Learning. arXiv Preprint arXiv:2406.08041. https://doi.org/10.48550/arXiv.2406.08041
[7]	Barndorff-Nielsen OE, Hansen PR, Lunde A, et al. (2009) Realized kernels in practice: Trades and quotes. Economet J. https://doi.org/10.1111/j.1368-423X.2008.00275.x
[8]	Barndorff-Nielsen OE, Kinnebrok S, Lunde A, et al. (2009) Measuring downside risk-realised semivariance. CREATES Res Pap. 2008–42. http://dx.doi.org/10.2139/ssrn.1262194
[9]	Barndorff-Nielsen OE, Shephard N (2004) Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica 72: 885–925. https://doi.org/10.1111/j.1468-0262.2004.00515.x doi: 10.1111/j.1468-0262.2004.00515.x
[10]	Bayer Christian, Friz PK, Fukasawa M, et al. (2023) Rough volatility. SIAM
[11]	Blom HM, de Lange PE, Risstad M (2023) Estimating Value-at-Risk in the EURUSD Currency Cross from Implied Volatilities Using Machine Learning Methods and Quantile Regression. J Risk Financ Manag 16: 312. https://doi.org/10.3390/jrfm16070312 doi: 10.3390/jrfm16070312
[12]	Bollerslev T, Patton AJ, Quaedvlieg R (2016) Exploiting the errors: A simple approach for improved volatility forecasting. J Econom 192: 1–18. https://doi.org/10.1016/j.jeconom.2015.10.007 doi: 10.1016/j.jeconom.2015.10.007
[13]	Branco R, Rubesam A, Zevallos M (2024) Forecasting realized volatility: Does anything beat linear models? J Empir Financ 2024: 101524. https://doi.org/10.1016/j.jempfin.2024.101524
[14]	Clements A, Preve D (2021) A practical guide to harnessing the HAR volatility model. J Bank Financ 133: 106285. https://doi.org/10.1016/j.jbankfin.2021.106285 doi: 10.1016/j.jbankfin.2021.106285
[15]	Corsi F (2009) A simple approximate long-memory model of realized volatility. J Financ Economet 7: 174–196. https://doi.org/10.1093/jjfinec/nbp001 doi: 10.1093/jjfinec/nbp001
[16]	Götz P (2023) Realized quantity extended conditional autoregressive Value-at-Risk models. J Risk 26.
[17]	Liang C, Li Y, Ma F, et al. (2022) Forecasting international equity market volatility: A new approach. J Forecast 41: 1433–1457.
[18]	Gunnarsson ES, Isern HR, Kaloudis A, et al. (2024) Prediction of realized volatility and implied volatility indices using AI and machine learning: A review Int Rev Financ Anal 2024: 103221 https://doi.org/10.1016/j.irfa.2024.103221
[19]	de Lange PE, Risstad M, Westgaard S (2022) Estimating value-at-risk using quantile regression and implied volatilities. J Risk Model Validat.
[20]	Liu LY, Patton AJ, Sheppard K (2015) Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes. J Econom 187: 293–311. https://doi.org/10.1016/j.jeconom.2015.02.008 doi: 10.1016/j.jeconom.2015.02.008
[21]	Liu G, Wei Y, Chen Y, et al. (2018) Forecasting the value-at-risk of Chinese stock market using the HARQ model and extreme value theory. Physica A 499: 288–297. https://doi.org/10.1016/j.physa.2018.02.033 doi: 10.1016/j.physa.2018.02.033
[22]	Lyócsa S, Molnár P, Fedorko I (2016) Forecasting exchange rate volatility: The case of the Czech Republic, Hungary and Poland. Financ Uver 66: 453–463.
[23]	Lyócsa S, Plíhal T, Vỳrost T (2024) Forecasting day-ahead expected shortfall on the EUR/USD exchange rate: The (I) relevance of implied volatility. Int J Forecast. https://doi.org/10.1016/j.ijforecast.2023.11.003
[24]	Ma F, Wahab M, Zhang Y (2019) Forecasting the US stock volatility: An aligned jump index from G7 stock markets. Pac-Basin Financ J 54: 132–146. https://doi.org/10.1016/j.pacfin.2019.02.006 doi: 10.1016/j.pacfin.2019.02.006
[25]	Newey WK, West KD (1987) Hypothesis testing with efficient method of moments estimation. Int Econom Rev 54: 777–787. https://doi.org/10.2307/2526578 doi: 10.2307/2526578
[26]	Pascalau R, Poirier R (2023) Increasing the information content of realized volatility forecasts. J Financ Econom 21: 1064–1098. https://doi.org/10.1093/jjfinec/nbab028 doi: 10.1093/jjfinec/nbab028
[27]	Patton AJ (2011) Volatility forecast comparison using imperfect volatility proxies. J Econom 160: 246–256. https://doi.org/10.1016/j.jeconom.2010.03.034 doi: 10.1016/j.jeconom.2010.03.034
[28]	Patton AJ, Sheppard K (2015) Good volatility, bad volatility: Signed jumps and the persistence of volatility. Rev Econom Stat 97: 683–697. https://doi.org/10.1162/REST_a_00503 doi: 10.1162/REST_a_00503
[29]	Plíhal Tomáš, Lyócsa Štefan (2021) Modeling realized volatility of the EUR/USD exchange rate: Does implied volatility really matter? Int Rev Econom Financ 71: 811–829. https://doi.org/10.1016/j.iref.2020.10.001
[30]	Qiu Y, Wang Z, Xie T, et al. (2021) Forecasting Bitcoin realized volatility by exploiting measurement error under model uncertainty. J Empir Financ 62: 179–201. https://doi.org/10.1016/j.jempfin.2021.03.003 doi: 10.1016/j.jempfin.2021.03.003
[31]	Qu H, Duan Q, Niu M (2018) Modeling the volatility of realized volatility to improve volatility forecasts in electricity markets. Energ Econ 74: 767–776. https://doi.org/10.1016/j.eneco.2018.07.033 doi: 10.1016/j.eneco.2018.07.033
[32]	Rokicka A, Kudła J (2020) Modeling Realized Volatility with Implied Volatility for the EUR/GBP Exchange Rate markets. J Risk 23.
[33]	Risstad M, Thodesen A, Thune KA, et al. (2023) On the Exchange Rate Dynamics of the Norwegian Krone. J Risk Financ Manag 16: 308. https://doi.org/10.3390/jrfm16070308
[34]	Shen D, Urquhart A, Wang P (2020) Forecasting the volatility of Bitcoin: The importance of jumps and structural breaks. Eur Financ Manag 26: 1294–1323. https://doi.org/10.1111/eufm.12254 doi: 10.1111/eufm.12254
[35]	Salmon N, SenGupta I (2021) Fractional Barndorff-Nielsen and Shephard model: Applications in variance and volatility swaps, and hedging. Ann Financ 17: 529–558. https://doi.org/10.1007/s10436-021-00394-4 doi: 10.1007/s10436-021-00394-4
[36]	Sizova N (2011) Integrated variance forecasting: Model based vs. reduced form. J Econom 162: 294–311. https://doi.org/10.1016/j.jeconom.2011.02.004 doi: 10.1016/j.jeconom.2011.02.004
[37]	Swanson NR, White H (1997) Forecasting economic time series using flexible versus fixed specification and linear versus nonlinear econometric models. Int J Forecast 13: 439–461. https://doi.org/10.1016/S0169-2070(97)00030-7 doi: 10.1016/S0169-2070(97)00030-7
[38]	Wang Y, Liang F, Wang T, et al. (2020) Does measurement error matter in volatility forecasting? Empirical evidence from the Chinese stock market. Econ Model 87: 148–157. https://doi.org/10.1016/j.econmod.2019.07.014 doi: 10.1016/j.econmod.2019.07.014
[39]	White H (1980) DA heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 1980: 817–838. https://doi.org/10.2307/1912934 doi: 10.2307/1912934

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)