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Is energy risk scale Invariant? evidence from crude oil futures

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  • Grobys, Klaus

Abstract

This study diverges from earlier research by utilizing power-law functions to model realized variances in crude oil prices and analyzing these functions across various time scales. The findings reveal several key insights. First, uncertainty in crude oil markets exhibits fractal-like properties, manifested in scale invariant power-law behavior. Second, the estimated power-law exponent demonstrates invariance in the intertemporal dimension, a result confirmed through the test for total invariance, which did not reject the hypothesis of total invariance in power-law behavior. Third, the study provides evidence that the variance of crude oil price variance is statistically infinite, rendering sample variance estimates inherently context-dependent. Fourth, in contrast to earlier literature supporting the lognormal model, the findings decisively reject the lognormal model as a valid data-generating process for realized crude oil price variances across all time scales. These results have significant theoretical and practical implications. The fractal properties and infinite variance challenge conventional assumptions about crude oil market dynamics, while the rejection of the lognormal model highlights the need for alternative frameworks in modeling and risk management.

Suggested Citation

  • Grobys, Klaus, 2025. "Is energy risk scale Invariant? evidence from crude oil futures," The North American Journal of Economics and Finance, Elsevier, vol. 80(C).
    • Handle: RePEc:eee:ecofin:v:80:y:2025:i:c:s1062940825001160
    DOI: 10.1016/j.najef.2025.102476
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    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. John W. Galbraith, 2004. "Circuit Breakers and the Tail Index of Equity Returns," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 109-129.
    3. Fathi, Masoumeh & Grobys, Klaus & Äijö, Janne, 2025. "A common component of Fama and French factor variances," The North American Journal of Economics and Finance, Elsevier, vol. 75(PA).
    4. Jinghong Shu & Jin E. Zhang, 2006. "Testing range estimators of historical volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(3), pages 297-313, March.
    5. Mohammadi, Hassan & Su, Lixian, 2010. "International evidence on crude oil price dynamics: Applications of ARIMA-GARCH models," Energy Economics, Elsevier, vol. 32(5), pages 1001-1008, September.
    6. Grobys, Klaus, 2023. "Correlation versus co-fractality: Evidence from foreign-exchange-rate variances," International Review of Financial Analysis, Elsevier, vol. 86(C).
    7. Gao, Xin & Li, Bingxin & Liu, Rui, 2023. "The relative pricing of WTI and Brent crude oil futures: Expectations or risk premia?," Journal of Commodity Markets, Elsevier, vol. 30(C).
    8. Fang, Ying & Fan, Ying & Haroon, Muhammad & Dilanchiev, Azer, 2023. "Exploring the relationship between global economic policy and volatility of crude futures: A two-factor GARCH-MIDAS analysis," Resources Policy, Elsevier, vol. 85(PA).
    9. Grobys, Klaus, 2024. "A universal exponent governing foreign exchange rate risks," International Review of Financial Analysis, Elsevier, vol. 95(PB).
    10. Huang, Bwo-Nung & Hwang, M.J. & Peng, Hsiao-Ping, 2005. "The asymmetry of the impact of oil price shocks on economic activities: An application of the multivariate threshold model," Energy Economics, Elsevier, vol. 27(3), pages 455-476, May.
    11. Carmela Quintos & Zhenhong Fan & Peter C. B. Phillips, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 633-663.
    12. repec:aen:journl:1995v16-04-a02 is not listed on IDEAS
    13. Sadorsky, Perry, 1999. "Oil price shocks and stock market activity," Energy Economics, Elsevier, vol. 21(5), pages 449-469, October.
    14. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    15. Sadorsky, Perry, 2003. "The macroeconomic determinants of technology stock price volatility," Review of Financial Economics, Elsevier, vol. 12(2), pages 191-205.
    16. Roger D. Huang & Ronald W. Masulis & Hans R. Stoll, 1996. "Energy shocks and financial markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 16(1), pages 1-27, February.
    17. Joshua McGillivray & Anatoliy Swishchuk, 2024. "Variance-Hawkes Process and its Application to Energy Markets," Papers 2410.08420, arXiv.org.
    18. Mengxi He & Yaojie Zhang & Yudong Wang & Danyan Wen, 2024. "Modelling and forecasting crude oil price volatility with climate policy uncertainty," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 11(1), pages 1-10, December.
    19. Peter Ferderer, J., 1996. "Oil price volatility and the macroeconomy," Journal of Macroeconomics, Elsevier, vol. 18(1), pages 1-26.
    20. Cheong, Chin Wen, 2009. "Modeling and forecasting crude oil markets using ARCH-type models," Energy Policy, Elsevier, vol. 37(6), pages 2346-2355, June.
    21. Robert S. Pindyck, 1999. "The Long-Run Evolution of Energy Prices," The Energy Journal, , vol. 20(2), pages 1-27, April.
    22. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2010. "Forecasting crude oil market volatility: Further evidence using GARCH-class models," Energy Economics, Elsevier, vol. 32(6), pages 1477-1484, November.
    23. Plourde, André & Watkins, G. C., 1998. "Crude oil prices between 1985 and 1994: how volatile in relation to other commodities?," Resource and Energy Economics, Elsevier, vol. 20(3), pages 245-262, September.
    24. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    25. Chen, Shiu-Sheng & Chen, Hung-Chyn, 2007. "Oil prices and real exchange rates," Energy Economics, Elsevier, vol. 29(3), pages 390-404, May.
    26. Thomas Werner & Christian Upper, 2004. "Time variation in the tail behavior of Bund future returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(4), pages 387-398, April.
    27. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    28. Yang, C. W. & Hwang, M. J. & Huang, B. N., 2002. "An analysis of factors affecting price volatility of the US oil market," Energy Economics, Elsevier, vol. 24(2), pages 107-119, March.
    29. Sadorsky, Perry, 2006. "Modeling and forecasting petroleum futures volatility," Energy Economics, Elsevier, vol. 28(4), pages 467-488, July.
    30. Linya Huang & Xite Yang & Yongzeng Lai & Ankang Zou & Jilin Zhang, 2024. "Crude Oil Futures Price Forecasting Based on Variational and Empirical Mode Decompositions and Transformer Model," Mathematics, MDPI, vol. 12(24), pages 1-16, December.
    31. Perry Sadorsky, 2003. "The macroeconomic determinants of technology stock price volatility," Review of Financial Economics, John Wiley & Sons, vol. 12(2), pages 191-205.
    32. Kiseok Lee & Shawn Ni & Ronald A. Ratti, 1995. "Oil Shocks and the Macroeconomy: The Role of Price Variability," The Energy Journal, , vol. 16(4), pages 39-56, October.
    33. Renò, Roberto & Rizza, Rosario, 2003. "Is volatility lognormal? Evidence from Italian futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 620-628.
    34. Kang, Sang Hoon & Kang, Sang-Mok & Yoon, Seong-Min, 2009. "Forecasting volatility of crude oil markets," Energy Economics, Elsevier, vol. 31(1), pages 119-125, January.
    35. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G19 - Financial Economics - - General Financial Markets - - - Other

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