Source-linked AI summary
Co-movement of energy commodities revisited: Evidence from wavelet coherence analysis
Lukas Vacha, Jozef Barunik
TL;DR
The paper addresses limited analysis of energy-commodity co-movement across both time and investment horizons. It uses wavelet coherence as a model-free time-frequency approach, compares it with DCC GARCH, and finds strongly time-varying dependence among some energy pairs, especially around sharp price declines.
Problem
Energy-market interconnections are often analyzed separately in time or frequency, leaving their joint time-frequency dynamics insufficiently characterized.
Method
The paper applies squared wavelet coherence to crude oil, gasoline, heating oil, and natural gas and compares the results with DCC GARCH.
Results
Some energy pairs exhibit strong co-movement dynamics across time and investment horizons, with the strongest dependence occurring during sharp price drops.
Takeaways & Limitations
Dependence should be assessed as time-varying and across investment horizons because the heating oil–gasoline–crude oil trio can imply substantial portfolio risk, while natural gas appears unrelated.
Takeaways & Limitations
Forecasting with wavelet coherence is difficult in this setting because of the nature of wavelets.
Abstract
from arXiv · showhide
In this paper, we contribute to the literature on energy market co-movement by studying its dynamics in the time-frequency domain. The novelty of our approach lies in the application of wavelet tools to commodity market data. A major part of economic time series analysis is done in the time or frequency domain separately. Wavelet analysis combines these two fundamental approaches allowing study of the time series in the time- frequency domain. Using this framework, we propose a new, model-free way of estimating time-varying cor- relations. In the empirical analysis, we connect our approach to the dynamic conditional correlation approach of Engle (2002) on the main components of the energy sector. Namely, we use crude oil, gasoline, heating oil, and natural gas on a nearest-future basis over a period of approximately 16 and 1/2 years beginning on November 1, 1993 and ending on July 21, 2010. Using wavelet coherence, we uncover interesting dynamics of correlations between energy commodities in the time-frequency space.
1. Introduction
Energy commodities matter for diversification, industrial decisions, and interconnected market dynamics, but their time-series behavior spans multiple frequencies. The paper therefore applies wavelets to examine commodity interdependence jointly across time and frequency, alongside standard econometric tools.
- Motivation: Energy commodity prices affect diverse markets, market participants, and industrial decision-making, making their dynamics and interconnections important to understand.They also exhibit more extreme statistical properties than several traditional financial assets.
- Research gap: Commodity-market time series combine components operating at different frequencies, while standard econometric methods usually separate frequency and time analysis.Wavelets retain time information while studying frequency components.
- Related work: Prior energy-market research includes commodity-specific dynamics, macroeconomic relationships, and co-movement studies, including work on dynamic conditional correlations.Earlier wavelet correlation research on oil prices and economic activity was restricted to monthly data and longer cycles.
- Research question: The paper asks whether interconnections between energy commodities change over time and vary across investment horizons.The approach is presented as a more interpretable contribution to co-movement research.
- Approach: Wavelet coherence is applied to crude oil, gasoline, heating oil, and natural gas to estimate dynamic correlations across time and frequencies.The framework distinguishes investor horizons and separates cyclical components across time periods.
- Study design: The study presents wavelet coherence for local time-frequency correlations and compares it with the DCC GARCH model.The empirical analysis uses energy-market data and reports results after introducing these methods.
2. Methodology
The methodology uses continuous wavelet tools to measure local co-movement and phase relationships across time and frequency, then connects these estimates with DCC-GARCH correlations. Wavelet coherence identifies dependence patterns, while phase differences indicate synchronization and lead–lag structure.
- Wavelet framework: Continuous wavelet analysis decomposes time series into localized frequency components while retaining time information.The approach is suited to locally stationary and inhomogeneous series.
- Wavelet framework: The Morlet wavelet is used with central frequency ω0 = 6, and its complex form permits analysis of both amplitude and phase.The wavelet’s location and scale parameters determine position and frequency resolution.
- Wavelet coherence: The cross wavelet transform combines the continuous transforms of two series, while cross wavelet power identifies local covariance and common power across scales.The position index is u, scale is s, and the asterisk denotes complex conjugation.
- Wavelet coherence: Squared wavelet coherence measures local linear correlation between two series at each scale, with values from 0 to 1 indicating weak to strong correlation.Smoothing is required because unsmoothed coherence equals one at all scales; significance is tested with Monte Carlo methods.
- Boundary conditions: Finite sample boundaries create edge effects in wavelet transforms, represented by the cone of influence after zero-padding the time series.The cone’s location depends on the wavelet type.
- Phase differences: Phase differences describe delays between oscillations: rightward arrows indicate in-phase or positive correlation, leftward arrows indicate anti-phase or negative correlation, and vertical direction identifies leads.An upward arrow means the first series leads by 90°, whereas a downward arrow means the second series leads by 90°.
- DCC-GARCH comparison: The analysis compares local time-varying correlations from wavelet coherence with Engle’s Dynamic Conditional Correlation GARCH model.The DCC model allows the correlation matrix to vary over time and imposes α + β < 1.
3. Empirical results
The empirical analysis finds strong but highly dynamic co-movement among energy commodities, varying across both time and investment horizons. Wavelet coherence reveals patterns that complement standard correlation and DCC GARCH comparisons.
- Data description: The sample contains 3,573 daily prices for crude oil, gasoline, heating oil, and natural gas from November 1, 1993, to July 21, 2010.
- Unconditional correlations: Heating oil, crude oil, and gasoline show high unconditional correlations, while natural gas has the weakest dependence on the other commodities.Heating oil has the strongest relationship with crude oil; the three strongest pairs have positive correlations of around 0.6.
- Wavelet coherence: Wavelet coherence identifies significant co-movement across time-frequency regions, with warmer colors indicating stronger dependence and black boundaries marking significance.The analysis covers scales from one day to approximately one market year and uses Monte Carlo simulations for significance assessment.
- Wavelet coherence: Heating oil, gasoline, and crude oil exhibit the strongest dependence, whereas relationships involving natural gas contain only very small significant areas.Heating oil and crude oil are strongly related across many periods and frequencies; heating oil–gasoline dependence is restricted to selected periods.
- Time-frequency dynamics: Dependence changes rapidly over time and frequency, and short periods with changing phases do not support a consistent conclusion about directional influence.The study therefore distinguishes co-movement patterns across investment horizons without concluding that one commodity consistently leads another.
4. Concluding remarks
The paper finds that energy-commodity co-movement varies over time and across investment horizons. Heating oil, gasoline, and crude oil co-move strongly, while natural gas remains largely unrelated.
- Energy-pair co-movement changes substantially over time and across investment horizons.The authors characterize these dynamics as strong for some energy pairs.
- Heating oil, gasoline, and crude oil show strong co-movement, implying substantial portfolio exposure to their shared risk.
- Natural gas appears unrelated to the other three commodities across the studied horizons and periods.
- 64 to 128-day cycles occur in the heating oil–crude oil pair even during stable-growth periods.
- The findings are model-free and suggest that dynamic diversification is required to preserve higher profit.
Appendix A
Appendix A reports descriptive statistics and multivariate DCC GARCH coefficient estimates for the four energy commodities over the study period.
- Table 2 reports descriptive statistics for daily logarithmic returns of heating oil, gasoline, natural gas, and crude oil.
- The reported return statistics cover November 1, 1993 to July 21, 2010.
- Table 3 reports multivariate DCC GARCH coefficient estimates for the four energy commodities.The caption identifies αDCC and βDCC as coefficients from Equation 12.