Analysis of Self-Similarity in Short and Long Movements of Crude Oil Prices by Combination of Stationary Wavelet Transform and Range-Scale Analysis: Effects of the COVID-19 Pandemic and Russia-Ukraine War
Abstract
1. Introduction
- (a)
- Self-similarity is examined in prices of two major crude oil markets, namely Brent and WTI.
- (b)
- The effect of the COVID-19 pandemic and the Russia-Ukraine war on self-similarity is examined. A calm period is considered a reference period.
- (c)
- We propose to combine SWT and R/S analysis to better analyze the data by estimating the Hurst exponent in the SWT domain.
- (d)
- Self-similarity is estimated from short and long movements in prices for better understanding of the dynamics of price series under different extreme events.
- (e)
- (f)
- The study should provide traders and investors with insightful directions regarding investment in crude oil markets during times of major crises.
2. Materials and Methods
2.1. Stationary Wavelet Transform
2.2. R/S Analysis
3. Results
4. Discussion and Conclusions
Funding
Data Availability Statement
Conflicts of Interest
References
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Brent Movements | WTI Movements | |||
---|---|---|---|---|
Long | Short | Long | Short | |
Periods | ||||
Calm | 0.9339 | 0.2726 | 0.9024 | 0.3032 |
Pandemic | 1.0223 | 0.3094 | 1.0062 | 0.342 |
War | 0.9756 | 0.1931 | 0.9557 | 0.2875 |
Change rate | ||||
Calm–pandemic | 9% | 13% | 12% | 13% |
Pandemic–war | −5% | −38% | −5% | −16% |
Study | Purpose | Period | Findings |
---|---|---|---|
[21] | Examine the random walk hypothesis in Brent and WTI returns. | June 1982 to July 2008 | The Brent crude oil market is weak-form efficient, while the WTI crude oil market seems to be inefficient in the 1994–2008 sub-period. |
[22] | Examine long-range correlation in Brent returns. | May 1987 to September 2012 | Presence of long-range correlation in returns. After the financial crisis of 2008, the Brent crude oil market becomes more persistent. |
[23] | Examine long-range correlation in Brent and WTI returns. | May 1987 to September 2012 | Crude oil price shock sequences exhibit long-range correlations. |
[24] | Examine multifractal in WTI | Apr 1986 to June 2018 | The WTI market shows multifractality. Sources of multifractality are from long-range correlations and fat-tailed distributions. |
[25] | Examine chaos in Brent and WTI | November 1998 to March 2016 | No evidence of chaos in prices and returns in Brent and WTI before and after the financial crisis. Strong evidence of chaos in the volatility of Brent and WTI after the financial crisis. |
[26] | Examine long memory in WTI crude oil futures | April 1983 to October 2012 | The WTI oil futures market is weak-form efficient during the entire period. It is inefficient right after the crashes (1985, 2008) and the Gulf War. |
[27] | Examine correlation dimension, Lyapunov exponent, and approximate entropy for the periods before and during the COVID-19 pandemic in Brent and WTI, among others. | November 2017 to November 2022 | The COVID-19 pandemic affected WTI, Brent, and gas markets. |
[28] | Investigate causality between international fossil energy markets and the effect of the COVID-19 pandemic on their clustering structures. | August 1993 to June 2023 | The COVID-19 pandemic significantly affected information transmission between fossil energy markets and altered the microstructure of fossil energy markets. |
[29] | Investigate the impact of the COVID-19 outbreak on crude oil market efficiency. | January 2000 to April 2022 | The WTI market was efficient most of the time in the years before the COVID-19 pandemic. However, it was not efficient in some major periods during the pandemic. |
[30] | Investigate the connectedness between the 10 most traded cryptocurrencies and gold as well as crude oil markets pre-COVID-19 and during COVID-19. | January 2019 to December 2020 | Before the COVID-19 pandemic, the causal relationship predominantly flowed from gold and crude oil (Brent and WTI) toward the cryptocurrency markets. During the COVID-19 period, the direction of causality shifted, with cryptocurrencies exerting influence on the gold and crude oil markets. |
[31] | Examine multiscale fractals and entropy in fossil energy markets. | November 2017 to November 2022 | The COVID-19 pandemic affected multifractal behavior and multiscale entropy characteristics in WTI, Brent, gasoline, and heating oil markets. |
Our study | To decompose price time series of Brent and WTI by SWT to obtain their corresponding long and short movements. To estimate long memory in the decomposed series for better characterization and understanding of their dynamics. | January 2018 to September 2024 | Both COVID-19 and the Russia-Ukraine war significantly affected long memory in the short and long movements of Brent and WTI prices. |
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Lahmiri, S. Analysis of Self-Similarity in Short and Long Movements of Crude Oil Prices by Combination of Stationary Wavelet Transform and Range-Scale Analysis: Effects of the COVID-19 Pandemic and Russia-Ukraine War. Fractal Fract. 2025, 9, 176. https://doi.org/10.3390/fractalfract9030176
Lahmiri S. Analysis of Self-Similarity in Short and Long Movements of Crude Oil Prices by Combination of Stationary Wavelet Transform and Range-Scale Analysis: Effects of the COVID-19 Pandemic and Russia-Ukraine War. Fractal and Fractional. 2025; 9(3):176. https://doi.org/10.3390/fractalfract9030176
Chicago/Turabian StyleLahmiri, Salim. 2025. "Analysis of Self-Similarity in Short and Long Movements of Crude Oil Prices by Combination of Stationary Wavelet Transform and Range-Scale Analysis: Effects of the COVID-19 Pandemic and Russia-Ukraine War" Fractal and Fractional 9, no. 3: 176. https://doi.org/10.3390/fractalfract9030176
APA StyleLahmiri, S. (2025). Analysis of Self-Similarity in Short and Long Movements of Crude Oil Prices by Combination of Stationary Wavelet Transform and Range-Scale Analysis: Effects of the COVID-19 Pandemic and Russia-Ukraine War. Fractal and Fractional, 9(3), 176. https://doi.org/10.3390/fractalfract9030176