[Paper Review] Co-movement of energy commodities revisited: Evidence from wavelet coherence analysis

Lukáš Vácha, Jozef Baruník|RePEc: Research Papers in Economics|Jan 23, 2012

Market Dynamics and Volatility4 citations

TL;DR

This paper introduces a wavelet coherence approach to analyze time-varying correlations among energy commodities—crude oil, gasoline, heating oil, and natural gas—across multiple investment horizons. By combining time and frequency domain analysis without parametric assumptions, it reveals that co-movement is strongest during financial crises and periods of price declines, with crude oil, gasoline, and heating oil showing high dependence across frequencies, while natural gas remains largely uncorrelated.

ABSTRACT

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.

Motivation & Objective

• To investigate the dynamic co-movement of major energy commodities in both time and frequency domains, addressing limitations of traditional time- or frequency-only methods.
• To develop a model-free method for estimating time-varying correlations using wavelet coherence, avoiding parametric assumptions common in standard econometric models.
• To compare wavelet-based findings with the widely used DCC-GARCH model to validate and contextualize results in mainstream financial econometrics.
• To assess how different investment horizons (short-term, medium-term, long-term) influence the strength and evolution of correlations between energy markets.
• To identify structural shifts in market interdependence, particularly during financial crises and periods of economic stress, and their implications for portfolio risk management.

Proposed method

• Employs continuous wavelet transform (CWT) to decompose energy commodity returns into time-frequency components, preserving both temporal and spectral information.
• Uses wavelet coherence to estimate local correlation between pairs of commodities in the time-frequency plane, quantifying both strength and phase relationships.
• Applies phase difference analysis to determine lead-lag relationships between commodity pairs, identifying directional dependencies in co-movement.
• Compares wavelet coherence results with dynamic conditional correlation (DCC) estimates from a multivariate GARCH model to validate findings and enhance interpretability.
• Analyzes daily returns of crude oil, gasoline, heating oil, and natural gas from November 1, 1993, to July 21, 2010, using a 16.5-year dataset.
• Utilizes MATLAB wavelet coherence package (provided by Grinsted) for robust computation of wavelet-based statistics and visualization of time-frequency dependencies.

Experimental results

Research questions

• RQ1 How do correlations between major energy commodities evolve over time and across different investment horizons?
• RQ2 What is the nature of lead-lag relationships between energy commodity pairs, and how do they vary by frequency?
• RQ3 Do periods of financial stress or market downturns exhibit significantly higher co-movement across commodities compared to stable market phases?
• RQ4 How does the wavelet coherence approach compare with the standard DCC-GARCH model in capturing time-varying correlations?
• RQ5 To what extent are natural gas returns correlated with crude oil, gasoline, and heating oil across various time scales and market conditions?

Key findings

• Crude oil, gasoline, and heating oil exhibit strong, time-varying co-movement across multiple frequencies, especially during financial crises (2001–2002 and 2008–2010), with coherence persisting across short-, medium-, and long-term horizons.
• The gasoline–crude oil pair shows significant dependence at several-month investment horizons during 1997–2001, while short-term correlations remain low, indicating frequency-specific dynamics.
• The heating oil–crude oil pair displays persistent long cycles (64–128 days) in coherence, even during periods of stable growth, suggesting structural frequency dependence beyond crisis periods.
• Natural gas shows no significant coherence with the other three commodities across any investment horizon or time period, indicating its relative independence in the energy market.
• Wavelet coherence reveals that market complexity decreases during downturns (as shown by reduced entropy), correlating with increased co-movement and stronger dependence across horizons.
• The DCC-GARCH model estimates yield αDCC = 0.0444 and βDCC = 0.9006, indicating high persistence in conditional correlations, which aligns with the wavelet findings of sustained co-movement during crises.