Efficiency of Base Metal Futures Markets: Evidence Using Non-linear Models

Abstract

This study examines the efficiency of base metal futures traded on the London Metal Exchange, the New York Mercantile Exchange, the Multi Commodity Exchange of India, and the Shanghai Futures Exchange using daily aluminium and copper prices from 1 January 2015 to 30 September 2025. The analysis draws on both parametric measures, namely information share and component share, and non-parametric approaches, including Shannon and Rényi Transfer Entropy. To further account for time variation and structural changes, the analysis is extended using a Markov-switching vector autoregressive (MS-VAR) model and a time-varying parameter VAR framework, enabling the identification of regime-dependent, continuously evolving dynamics in information transmission. The study supports the transaction cost theory by showing that futures markets play a dominant role in price discovery and are likely to serve as the primary venue for this process, given their lower transaction costs and higher liquidity relative to spot markets. The results from Rényi entropy show that the relationship between futures and spot prices changes as greater weight is given to tail events. At the same time, the MS-VAR model further supports the adaptive market hypothesis by indicating that market efficiency varies across market conditions.

Keywords

Base metals futures adaptive market hypothesis Transfer Entropy price discovery non-linear model

1. Introduction

Base metals such as aluminium and copper are fundamental to global industrial production and economic activity due to their widespread use across sectors. However, their prices are inherently volatile, as they are influenced by fluctuations in demand and supply and changing market conditions (Jhunjhunwala & Suresh, 2020). To manage this uncertainty, the development of base metals futures markets has provided participants with an effective tool to hedge against price risk and actively manage their exposure (Sharma & Karmakar, 2024). The benefits of using base metals futures are evident, particularly in facilitating price discovery and creating a more robust economic environment.

According to the World Federation of Exchanges report, base-metal futures trading volumes have steadily fallen since 2016. Between 2018 and 2019, trading volume plunged 61%, falling from 1.52 billion to 587.6 million contracts. The decline in trading volume raises concerns, as trading volume is a key indicator of market success. It raises questions about the efficiency of the futures market, as lower participation may signal reduced investor confidence. Therefore, it is crucial to assess the base metal futures market from an efficiency perspective.

A market is considered efficient when information flows freely and is quickly reflected in prices. This idea is based on the assumption that investors act rationally by using available information to make decisions (Dash et al., 2025). Fama (1970) suggests that financial markets adjust to new information in a way that supports efficiency. As a result, any information that affects the value of a security is rapidly incorporated into its price (Hu & Lee, 2024), leading to quick price adjustments. Such price adjustments often occur across related markets, where the flow of information reflects their degree of integration and helps identify which market plays a leading role (Kia et al., 2026; Rout et al., 2024). Futures markets play an important role in this process by facilitating price discovery by incorporating expectations of future spot prices (Gupta et al., 2018). This leading role of futures markets can be explained by transaction cost theory (Islam et al., 2025; Yu et al., 2022), which argues that traders prefer markets with lower transaction costs and better trading conditions. With lower costs, greater liquidity and leverage, futures markets incorporate information faster than spot markets. As a result, both theoretical arguments and empirical evidence (Çağlı et al., 2019; Chen & Tongurai, 2022; Robertson & Zhang, 2025; Yu et al., 2022) consistently show that futures markets often lead in information transmission.

Previous studies on futures–spot dynamics use parametric models that assume a linear relationship between futures and the spot markets (Gupta et al., 2018; Kantamaneni & Asi, 2023; Karmakar & Inani, 2019; Rout et al., 2024). Granger causality is the most common tool for detecting lead–lag effects, but it relies on assumptions about the underlying stochastic processes. However, merely identifying the direction of information flow is not sufficient for making well-informed decisions, and the Granger causality approach has its limitations. Recent studies (Ameur et al., 2022; Guo et al., 2020; Li & Chavas, 2023) provide evidence of non-linear relationships between spot and futures returns, suggesting that earlier research may have overlooked these dynamics, leading to differing conclusions. To overcome this limitation, the present study adopts Transfer Entropy (TE), a non-parametric and model-free approach grounded in information theory (Marschinski & Kantz, 2002; Shannon, 1948). Recent studies have increasingly emphasized the usefulness of entropy-based approaches for evaluating market efficiency and information dynamics beyond traditional linear frameworks (Brouty & Garcin, 2023).

The present study extends the growing literature on market efficiency and information transmission by making several distinct contributions. First, while TE has been used to study financial asset–commodity linkages (Bekiros et al., 2017; Niu & Hu, 2021), no prior study has applied it to examine information flow between spot and futures prices of base metals across multiple exchanges. Second, we apply Rényi TE (RTE), an advancement over traditional linear models, to capture tail-dependent and non-linear information and quantify efficiency under normal and extreme market conditions. Third, prior studies have tested the adaptive market hypothesis (AMH) in markets such as crude oil (Wong et al., 2025), bond and equity markets (Tiwari et al., 2024) and precious metals (Shahid et al., 2020). However, the present study extends this literature by examining the AMH in base metal futures markets. Base metals provide a suitable setting for testing AMH because their link to real economic activity, sensitivity to global conditions, and exposure to shocks (e.g., crises, geopolitical events) suggest that market efficiency in base metals is likely to evolve over time. Therefore, examining AMH in this context helps capture the adaptive and time-varying nature of efficiency more effectively. By comparing entropy-based information, we provide direct evidence that efficiency in base metals is dynamic and exchange-specific, reflecting structural heterogeneity across markets. Finally, the study contributes to the broader commodity-finance literature by integrating information-theoretic and tail-risk perspectives into the analysis of futures market efficiency. This approach deepens understanding of how information diffuses between spot and futures markets.

The remainder of the article is organized as follows. Section 2 reviews the relevant literature on futures market efficiency. Section 3 outlines the methodology employed to assess the efficiency of the price discovery process. Section 4 presents and discusses the empirical findings. Finally, Section 5 concludes the study.

2. Literature Review

2.1. Why Revisiting Futures Market Efficiency

In recent decades, commodity markets have become increasingly complex due to structural changes in trading activity, participation and market integration. A growing body of literature documents that commodity futures markets are now more closely connected with broader financial markets and that trading behaviour has evolved beyond traditional hedging motives. While this study does not empirically examine financialization, these developments provide an important backdrop for reassessing the efficiency of futures markets.

The entry of financial investors, such as index traders, hedge funds and institutional participants, has altered traditional price discovery mechanisms by introducing speculative trading behaviour, portfolio-driven flows and cross-market linkages (Aït-Youcef & Joëts, 2024; Bohl et al., 2023). As a result, futures prices may no longer solely reflect fundamental supply–demand conditions, raising concerns about informational efficiency. As depicted in Figure 1, financialization influences commodity futures markets through three interrelated channels: structural shifts, pricing effects and market interlinkages. Structurally, the growing dominance of financial investors reduces hedging motives and increases noise trading and speculative bubbles, weakening the informational content of prices (Bohl et al., 2021). Pricing distortions (such as persistent contango, a more negative basis, and lower risk premiums) further impair the ability of futures prices to signal true market fundamentals (Chincarini & Moneta, 2021; Kang et al., 2023). At the same time, stronger correlations between commodities and financial assets reduce diversification benefits and transmit financial shocks into commodity markets (Aït-Youcef & Joëts, 2024). These mechanisms increase price volatility and undermine market efficiency by distorting price discovery and weakening the linkage between futures prices and underlying economic fundamentals (Goldstein & Yang, 2022). When futures markets become inefficient, they generate distorted price signals (Qian et al., 2025), compromise hedging effectiveness (Li & Xiong, 2024), and reduce the usefulness of commodities as risk management and diversification instruments (Dash et al., 2025).

Figure 1.

Conceptual Framework Depicting the Factors Influencing Market Efficiency.

Therefore, studying futures market efficiency is crucial for the reliability of futures prices for producers, consumers and policymakers. Evaluating efficiency provides key insights into whether futures markets continue to fulfil their core economic roles in an increasingly financialized trading environment.

2.2. Empirical Evidence on Futures Market Efficiency

Market efficiency attracts investors by ensuring prices reflect available information. Without this confidence, participation and volume decline, undermining price discovery and risk management. The efficiency of base-metal futures has been widely studied across major exchanges, largely through analyses of their price discovery role. Fernandez (2016) and Fung et al. (2010) demonstrate that the London Metal Exchange (LME), New York Mercantile Exchange (NYMEX) and Shanghai Futures Exchange (SHFE) futures generally reflect market fundamentals. There is a consistent relationship between futures and spot prices over time, indicating that the markets for these base metals are generally efficient in processing available information. Xiong and Li (2024) examined SHFE copper futures after the launch of International Energy Exchange bonded copper futures and found no significant impact on SHFE market efficiency. Their results show SHFE copper futures remain efficient despite the new international contracts, underscoring the market’s resilience and supporting the long-term efficiency of futures in price discovery. Figuerola-Ferretti and Gilbert (2005) noted that the LME’s aluminium futures show greater price transparency compared to COMEX. In contrast, Kenourgios and Samitas (2004) identified inefficiencies in LME copper futures. Bohl et al. (2021) examined the role of speculative traders in disrupting market efficiency and impairing the process by which markets respond to new information. The study found that Managed Money traders increased price volatility, leading to inefficiencies in futures markets during periods of economic uncertainty. Their findings demonstrated that speculative activities often lead to temporary mispricing, challenging the assumption of continuous market efficiency. Similarly, Fernandez (2010) found that base metal futures prices lack persistence, suggesting short-term inefficiencies and overreactions to information, primarily driven by speculative activity. In the Indian context, studies have shown a similar pattern of mixed efficiency. Sahoo and Kumar (2009) analyzed the Multi Commodity Exchange (MCX) futures markets for base metals and found that speculative activity and market illiquidity contributed to market inefficiencies. Their study concluded that the Indian futures markets have not yet reached the level of maturity observed in global markets, such as the LME or NYMEX, leading to more frequent inefficiencies. Similarly, Samal (2024) used linear models to examine the weak-form efficiency of base metal futures in India, concluding that these markets are inefficient, with spot and futures prices exhibiting long-run relationships but failing to pass the unbiasedness hypothesis. However, Thenmozhi and Thomas (2007) provided evidence supporting the efficiency of the MCX market, noting that despite periods of disruption, futures prices for copper and aluminium in India eventually reflect underlying supply–demand dynamics. Further, Rout et al. (2019) conclude that the base metal futures market in India generally supports efficient price discovery and effective volatility management.

Earlier studies exploring the relationship between futures and spot markets have predominantly relied on parametric models that assume a linear relationship between the returns of the two markets. Among these approaches, Granger causality has been the most widely used method for identifying lead–lag relationships, as it provides insights into the direction of information flow based on specific assumptions about the underlying stochastic processes. While this framework is useful for capturing directional dependence, it may not fully capture the complexity of interactions among markets. In particular, focusing solely on the direction of information transmission is often insufficient for drawing meaningful conclusions about market behaviour and efficiency. A key limitation of the Granger causality approach is its reliance on linearity and model-specific assumptions, which may limit its ability to capture the more complex dynamics of financial markets. Recent studies (Dergiades et al., 2018; Guo et al., 2020) provide evidence that spot–futures relationships are inherently non-linear, suggesting that earlier linear models may have overlooked important market dynamics and produced inconsistent conclusions. In light of these limitations, the present study employs TE to detect non-linear information flows between markets.

TE offers two significant advantages for estimating causal relationships. First, the key concept is the informational spillover dimension; therefore, it may not be necessary to consider the residual dimension (error terms) (Ji et al., 2019). Second, unlike Granger causality and other econometric methods, TE does not rely on stringent assumptions regarding the properties of time series, such as stationarity. This enables us to utilize ‘big data’ structures and provide more precise estimates. As a result, many studies have adopted TE and developed numerous variants to assess information transmission in economics and finance.

3. Data and Methodology

To evaluate the price discovery between spot and futures markets, we conduct an empirical analysis of the commodities traded on the LME, the MCX, the NYMEX, and the SHFE. Aluminium and copper were selected for their high trading volumes and availability across all exchanges. Lead was initially included, but the NYMEX lead showed no variation over the past 5 years, so it was dropped. The sample data of daily closing prices from 1 January 2015 to 30 September 2025 (2,086 observations) have been utilized in the study. The starting date is determined by data availability constraints, as consistent and continuous price series for aluminium futures on NYMEX are not available prior to 2015. Selecting this period ensures a balanced and comparable sample across exchanges, thereby avoiding inconsistencies arising from unequal data coverage. The end date corresponds to the most recent data available at the time of analysis, allowing the study to capture the latest market dynamics. We proceed with the analysis first, adjusting for missing values and ensuring the data set accounts for non-trading days and holidays.

Table 1 reports descriptive statistics for daily spot and futures returns on aluminium and copper across the LME, NYMEX, MCX and SHFE. Returns are generally low, with high volatility and strong non-normality, reflecting the risky nature of base metal markets. Mean returns are positive and similar between spot and futures within each exchange, indicating strong price linkage and limited arbitrage, particularly in the LME, MCX and SHFE. Volatility is higher on the LME and NYMEX, especially for copper, highlighting their role as global price leaders, while SHFE shows relatively lower volatility, possibly due to regulatory and domestic influences. Extreme values indicate significant downside risk, with NYMEX exhibiting the largest negative returns, and futures showing slightly wider ranges than spot markets. Skewness is mostly negative, suggesting greater downside risk, while excess kurtosis across all series confirms fat tails and deviation from normality, particularly in NYMEX. Overall, the results indicate integrated spot–futures markets with volatile, asymmetric and heavy-tailed return distributions.

Table 1.

Descriptive Statistics.

Commodity	Return	Mean	Std. Dev.	Min	Max	Skewness	Kurtosis
Aluminium LME	Spot	0.000109	0.000109	0.0129	−0.079	0.060	0.087
Aluminium LME	Futures	0.000108	0.000108	0.0126	−0.077	0.060	0.077
Aluminium NYMEX	Spot	0.000037	0.000037	0.0122	−0.201	0.067	−1.561
Aluminium NYMEX	Futures	0.000025	0.000025	0.0116	−0.201	0.109	−2.597
Aluminium MCX	Spot	0.000259	0.000259	0.0119	−0.094	0.105	0.162
Aluminium MCX	Futures	0.000263	0.000263	0.0110	−0.091	0.080	0.213
Aluminium SHFE	Spot	0.000172	0.000172	0.0089	−0.070	0.043	−0.637
Aluminium SHFE	Futures	0.000171	0.000171	0.0087	−0.060	0.050	−0.498
Copper LME	Spot	0.000160	0.000160	0.0128	−0.102	0.074	−0.243
Copper LME	Futures	0.000162	0.000162	0.0125	−0.081	0.069	−0.160
Copper MCX	Spot	0.000299	0.000299	0.0117	−0.074	0.074	−0.197
Copper MCX	Futures	0.000298	0.000298	0.0111	−0.074	0.043	−0.343
Copper NYMEX	Spot	0.000182	0.000182	0.0148	−0.249	0.124	−1.660
Copper NYMEX	Futures	0.000186	0.000186	0.0146	−0.246	0.123	−1.660
Copper SHFE	Spot	0.000200	0.000200	0.0092	−0.083	0.058	−0.315
Copper SHFE	Futures	0.000203	0.000203	0.0091	−0.084	0.052	−0.492

Note: LME: London Metal Exchange; MCX: Multi Commodity Exchange; NYMEX: New York Mercantile Exchange; SHFE: Shanghai Futures Exchange.

3.1. Information Share and Component Share

The study employs information share (IS) and component share (CS) to measure the contributions of spot and futures markets to price discovery. Both IS and the CS are based on the vector error correction model (VECM). The VECM framework is specified as:

Δ F t = δ f + α_{f} ε_{t} {_{-}}_{1} + β_{f} Δ F_{t}_{- 1} + ϒ f Δ S_{t}_{- 1} + ε_{f t}

(1)

Δ S t = δ s + α_{s} ε_{t} {_{-}}_{1} + β_{f} Δ S_{t}_{- 1} + ϒ s Δ F_{t}_{- 1} + ε_{s t}

(2)

Where α_f and α_s are the speed of adjustment and ε_t_–1 is the equilibrium error.

Based on the VECM framework, the IS, as proposed by Hasbrouck (1995), is used to measure each market’s contribution to price discovery. The IS bounds are computed as:

{IS}_{upper bound} = \frac{{(ψ_{1} σ_{1} + ψ_{2} ρ σ_{2})}^{2}}{{(ψ_{1} σ_{1} + ψ_{2} ρ σ_{2})}^{2} + ψ_{2}^{2} \cdot σ_{2}^{2} (1 - ρ^{2})}

(3)

{IS}_{lower bound} = \frac{ψ_{2}^{2} \cdot σ_{2}^{2} (1 - ρ^{2})}{{(ψ_{1} σ_{1} + ψ_{2} ρ σ_{2})}^{2} + ψ_{2}^{2} \cdot σ_{2}^{2} (1 - ρ^{2})}

(4)

$σ_{1}^{2}$ and $σ_{2}^{2}$ represent the variances of the VECM residuals for spot and futures prices, while ρ represents the contemporaneous correlation between these residuals.

CS evaluates the relative contribution of spot and futures markets to price discovery using the adjustment coefficients from the VECM:

{CS}_{S} = \frac{|α_{F}|}{|α_{F}| + |α_{S}|}

(5)

{CS}_{F} = \frac{|α_{S}|}{|α_{S}| + |α_{F}|}

(6)

3.2. Transfer Entropy: A Non-parametric Approach to Information Flow

To capture non-linear and directional information flows between spot and futures markets, the study employs TE, a non-parametric measure based on information theory (Schreiber, 2000). TE from futures to spot and from spot to futures are defined as:

\begin{matrix} T_{f \to s} = \sum & p (s_{t + 1}, s_{t}^{(k)}, f_{t}^{(l)}) log \frac{p (s_{t + 1} ∣ s_{t}^{(k)}, f_{t}^{(l)})}{p (s_{t + 1} ∣ s_{t}^{(k)})} \end{matrix}

(7)

\begin{matrix} T_{s \to f} = \sum & p (f_{t + 1}, f_{t}^{(k)}, s_{t}^{(l)}) log \frac{p (f_{t + 1} ∣ f_{t}^{(k)}, s_{t}^{(l)})}{p (f_{t + 1} ∣ f_{t}^{(k)})} \end{matrix}

(8)

Where $T_{f \to s} (T_{s \to f})$ is the information flow between futures (spot) and spot (futures), t represents the time, k and 1 represent the time delays or dimensions used to construct delay vectors from the processes S and f. The most natural choices for k and l are k = 1 and l = 1, respectively, which means using delay vectors of dimension 1. Comparing $T_{f \to s} and T_{s \to f}$ can help in determining the dominant direction of information transfer.

To account for tail-dependent information flows and extreme market conditions, the study further employs RTE:

{RT}_{f \to s} (k, l) = \frac{1}{1 - q} \log \frac{\sum_{i} ϕ_{q} (s_{t}^{(k)}) p^{q} (s_{t + 1} ∣ s_{t}^{(k)})}{\sum_{i, j} ϕ_{q} (s_{t}^{(k)}, f_{t}^{(l)}) p^{q} (s_{t + 1} ∣ s_{t}^{(k)}, f_{t}^{(l)})}

(9)

{RT}_{s \to f} (k, l) = \frac{1}{1 - q} log \frac{\sum_{i} ϕ_{q} (f_{t}^{(k)}) p^{q} (f_{t + 1} ∣ f_{t}^{(k)})}{\sum_{i, j} ϕ_{q} (f_{t}^{(k)}, s_{t}^{(l)}) p^{q} (f_{t + 1} ∣ f_{t}^{(k)}, s_{t}^{(l)})}

(10)

To correct for small-sample bias, effective TE (ETE) is calculated as:

{ETE}_{f \to s} (k, l) = T_{f \to s} (k, l) - T_{f shuffled \to s} (k, l)

(11)

{ETE}_{s \to f} (k, l) = T_{s \to f} (k, l) - T_{s shuffled \to f} (k, l)

(12)

Statistical significance is assessed using the Markov block bootstrap procedure.

Detailed methodological explanations for Sections 3.1 and 3.2 are provided in the supplementary file.

3.3. Markov-switching Vector Autoregression

The dynamic interactions among the variables are analyzed using a Markov-switching vector autoregression (MS-VAR) model, which extends the conventional VAR framework by allowing model parameters to vary across different unobserved regimes. Financial markets often experience structural shifts driven by changes in trading activity, information flows and market conditions, rendering the assumption of constant parameters unrealistic. The MS-VAR model addresses this issue by allowing the intercepts and autoregressive coefficients to vary with the prevailing regime, which is governed by a first-order Markov process. Formally, the model can be expressed as

Y_{t} = c_{S_{t}} + A_{S_{t}} Y_{t - 1} + ε_{t},

(13)

where $Y_{t}$ represents the vector of endogenous variables, $c_{S_{t}}$ and $A_{S_{t}}$ denote regime-dependent parameters, and $S_{t}$ is an unobserved state variable indicating the regime at time t. The transition between regimes is determined by a transition probability matrix, which captures the likelihood of remaining in or switching between regimes. The expected duration of each regime is derived from the diagonal elements of this matrix. A first-order lag specification is adopted to capture short-term dynamic interactions while maintaining a parsimonious model structure. The model is estimated using maximum likelihood techniques, and regime probabilities are obtained via the Hamilton filtering algorithm, enabling analysis of how relationships among variables evolve across different market regimes. The MS-VAR estimation is performed in MATLAB.

3.4. Time-varying Parameter Vector Autoregression

To enhance the robustness of the empirical findings, this study employs a time-varying parameter vector autoregression (TVP-VAR) model to examine the dynamic relationship between spot and futures markets. While the MS-VAR model captures regime-dependent changes in market dynamics, the TVP-VAR framework allows the coefficients to evolve continuously over time, thereby accounting for gradual structural changes in the transmission of information between markets. The model is specified as

Y_{t} = c_{t} + B_{t} Y_{t - 1} + ε_{t},

(14)

where the parameters are allowed to vary over time and follow a stochastic process. The model is estimated in a state-space form using the Kalman filter, which recursively updates the coefficients as new information becomes available. The TVP-VAR model is implemented in R using the ConnectednessApproach package.

4. Results and Discussions

This section presents results from both parametric and non-parametric models used in the study to assess the efficiency of the futures market through price discovery. Later, the section discusses the results using a rolling-window framework.

4.1. Price Discovery Through Parametric Models

The study examines the price discovery process for aluminium and copper using IS and CS measures. As a first step, a unit root test was performed to check the stationarity of the data, and the results indicate that all commodity series become stationary after first differencing. Following this, a cointegration test was conducted, confirming the existence of a long-run equilibrium relationship among the variables. The detailed results of both tests are provided in the supplementary file.

Both IS and CS are estimated within the VECM framework. The key parameters required include the coefficients of the error correction term (ECT), which capture the speed of adjustment, along with the standard deviations and correlation of the VECM residuals for spot and futures prices. While the CS approach relies only on the speed of adjustment coefficients, the IS measure additionally incorporates the residual variances and their correlation between spot and futures markets.

Table 2 details price discovery using IS and CS, where a contribution exceeding 50% indicates market dominance. For aluminium, spot markets generally lead on NYMEX, LME and SHFE, while MCX futures drive pricing in the Indian market. Conversely, copper futures dominate on NYMEX, LME and MCX, though SHFE spot markets maintain a very high CS contribution. The notable divergence between IS and CS values, especially for copper on SHFE and LME, stems from the distinct mathematical ways each method integrates VECM parameters, as discussed earlier.

Table 2.

Price Discovery Estimates Through Information and Component Share.

Commodity	Exchange	Market	IS	CS
Aluminium	NYMEX	Spot	0.607	0.541
Aluminium	NYMEX	Futures	0.393	0.459
Aluminium	LME	Spot	0.505	0.782
Aluminium	LME	Futures	0.495	0.218
Aluminium	MCX	Spot	0.473	0.354
Aluminium	MCX	Futures	0.527	0.646
Aluminium	SHFE	Spot	0.516	0.706
Aluminium	SHFE	Futures	0.484	0.294
Copper	NYMEX	Spot	0.499	0.479
Copper	NYMEX	Futures	0.501	0.521
Copper	LME	Spot	0.479	0.213
Copper	LME	Futures	0.521	0.787
Copper	MCX	Spot	0.488	0.332
Copper	MCX	Futures	0.512	0.668
Copper	SHFE	Spot	0.517	0.953
Copper	SHFE	Futures	0.483	0.046

Notes: IS denotes information share, and CS denotes component share. The IS presented in the table is the average of the upper bound and lower bound of the information share result. Higher values indicate a greater contribution of the respective market segment to price discovery. LME: London Metal Exchange; MCX: Multi Commodity Exchange; NYMEX: New York Mercantile Exchange; SHFE: Shanghai Futures Exchange.

4.2. Price Discovery Through Non-parametric Models

4.2.1. Shannon Transfer Entropy Results

The core question related to the futures market is its ability to perform its price discovery function efficiently. ETE can help determine the efficiency of the futures market in terms of price discovery. We implemented Shannon TE using the RTransferEntropy package, setting the embedding dimensions $(l x = l y = 1)$ to capture immediate past dependencies. Continuous data were discretized using quantile binning. To adjust for finite-sample bias, we applied ETE via surrogate shuffling (100 replications) and conducted inference using 300 bootstrap replications. Table 3 reports Shannon TE, measuring the direction and strength of non-linear information flow between spot and futures prices. Higher TE from futures to spot indicates futures-led price discovery, while higher TE from spot to futures suggests spot market leadership. Lower TE values imply weak information transmission and limited contribution to price discovery. The table also presents ETE, which adjusts TE for small-sample bias. However, in our results, ETE is consistently lower than TE, indicating that the estimated information flows are not dominated by noise.

Table 3.

Shannon Transfer Entropy Estimates.

Commodity	Exchange	Direction	TE	ETE	Std Error	p Value
Aluminium	NYMEX	Futures to spot	0.0000	0.0000	0.000	0.4167
Aluminium	NYMEX	Spot to futures	0.0000	0.0000	0.000	0.9233
Aluminium	LME	Futures to spot	0.0014	0.0000	0.0010	0.9900
Aluminium	LME	Spot to futures	0.0018	0.0000	0.0011	0.9533
Aluminium	MCX	Futures to spot	0.0056	0.0024	0.0012	0.0367
Aluminium	MCX	Spot to futures	0.0022	0.0000	0.0011	0.8367
Aluminium	SHFE	Futures to spot	0.0081	0.0048	0.0012	0.000
Aluminium	SHFE	Spot to futures	0.0036	0.0003	0.0011	0.3167
Copper	NYMEX	Futures to spot	0.0063	0.003	0.001	0.0033
Copper	NYMEX	Spot to futures	0.0063	0.0034	0.0011	0.0133
Copper	LME	Futures to spot	0.0031	0.000	0.001	0.4633
Copper	LME	Spot to futures	0.0016	0.000	0.001	0.9667
Copper	MCX	Futures to spot	0.0026	0.0000	0.0011	0.6333
Copper	MCX	Spot to futures	0.0034	0.0003	0.0011	0.3067
Copper	SHFE	Futures to spot	0.0038	0.0006	0.0011	0.2367
Copper	SHFE	Spot to futures	0.0094	0.0060	0.0010	0.000

Notes: p value indicates statistical significance. ETE: Effective Transfer Entropy; LME: London Metal Exchange; MCX: Multi Commodity Exchange; NYMEX: New York Mercantile Exchange; SHFE: Shanghai Futures Exchange.

For aluminium, the statistically significant information flow between the NYMEX and LME indicates weak directional dependence between the spot and futures markets. This outcome is consistent with highly liquid and mature trading environments, where active participation and arbitrage may lead to near-simultaneous price adjustment across market segments, leaving limited scope for persistent price leadership. In contrast, the futures-led price discovery observed on MCX, and especially on SHFE, may reflect differences in market structure and trading behaviour, in which futures markets play a more prominent role in aggregating information. For copper, bidirectional information flow on NYMEX indicates a mature, well-integrated market structure, whereas insignificant values on LME and MCX suggest episodic, weak information transmission. The strong spot-to-futures dominance on SHFE underscores the continued importance of physical market fundamentals in shaping futures prices.

4.2.2. Rényi Transfer Entropy Results

Commodity prices are primarily associated with extreme events, also known as tail events, characterized by large positive or negative returns. Saji and Paul (2026) define tail events as large market shocks or sudden price reversals that exhibit heavy-tailed, non-normal distributions. To account for the potential importance of tail events in the overall information flow, we employ RTE across quantiles (q) from 0.1 to 0.99. The parameter q adjusts sensitivity to these events, with lower values emphasizing tails. Figure 2 displays RTE estimates. Significant RTE indicates that knowledge of one market improves the informational efficiency of the other. While negative ETE suggests complex, non-linear dependencies rather than a lack of flow (Jizba et al., 2012), the results across all exchanges demonstrate that information transmission for aluminium and copper is significantly stronger during tail events than under normal market conditions.

Figure 2.

Note: RTE is estimated across quantiles (q) ranging from 0.1 to 0.99, where lower q values place greater emphasis on tail events. The left panel (X ↓ Y) shows information flow from futures to spot markets, while the right panel (Y ↓ X) shows the reverse. The red dashed line represents Shannon entropy, to which RTE converges as q approaches 1. Blue points denote RTE estimates, and blue bars represent 95% confidence intervals. Information flow is significant when the confidence intervals do not overlap with zero.

4.3. Price Discovery Through Rolling-window Analysis

Acknowledging the multistage nature of price discovery, we employ a rolling-window approach to analyze time-varying information transmission between spot and futures markets. Rolling estimation improves robustness to structural breaks (Liu & Su, 2019), though window selection remains important, as excessively short or long windows can distort results (Tang & Abosedra, 2016). Following prior studies (Xu, 2019; Xu et al., 2019), a 232-day rolling window is adopted.

To capture the rolling-window interactions between futures and spot prices, the study visualizes Shannon TE using a wavelet-based time–frequency framework and presented in Figure 3. The approach maps how information transfer evolves across time (horizontal axis) and across pseudo-periods or frequencies (vertical axis). Higher entropy values (warmer colours) indicate a stronger predictive influence, while significance (p < 0.05) is highlighted with masked overlays. The lower panels show the rolling TE series over time for both directions. This representation enables the identification of when (in time) and at what scale (in frequency) significant information flows occur, highlighting episodes of leadership or feedback between futures and spot markets.

Figure 3.

Note: The figure presents wavelet-based Shannon TE for 232-days rolling window. Warmer colours indicate stronger information transfer, while masked regions denote statistically significant TE values (p < 0.05). The lower panels show rolling TE for both directions of information flow, highlighting periods of market leadership and feedback effects.

Information transmission is clearly time-varying and frequency-dependent, confirming the multistage nature of price discovery. For aluminium traded on the LME and NYMEX, entropy is largely intermittent, indicating weak, episodic information flow with no persistent market dominance. In contrast, MCX and SHFE exhibit more frequent and sustained futures-to-spot information transmission, particularly across low- and medium-frequency bands. The rolling TE series further confirms that futures markets in these exchanges play a leading role in incorporating information over time. The rolling Shannon TE results for copper indicate largely bidirectional and episodic information flow on the LME and NYMEX, suggesting highly integrated futures and spot markets. In contrast, futures-to-spot transmission is more prominent on MCX, while spot-to-futures dominance is evident on SHFE, implying exchange-specific price discovery mechanisms in emerging markets.

4.4. Price Discovery Through Rolling-window Analysis with Shorter Window

To address sensitivity to window length, we extend the rolling analysis using a shorter 60-day window. While the 232-day window captures medium- to long-term dynamics, the shorter window allows examination of short-horizon information transmission and ensures results are not driven by window choice. Figure 4 presents 60-day rolling Shannon TE between spot and futures prices for aluminium and copper across exchanges. For aluminium, MCX and SHFE exhibit more frequent and persistent futures-to-spot information flows, indicating a stronger role for futures in short-term price discovery. In contrast, LME and NYMEX exhibit intermittent and bidirectional flows, suggesting rapid adjustment with no consistent leadership. For copper, MCX shows a relatively stronger but intermittent futures-to-spot transmission, whereas SHFE shows more frequent spot-to-futures flow, underscoring the role of physical market signals. The 60-day rolling analysis reinforces the robustness of the main findings and shows that futures markets become particularly informative.

Figure 4.

Note: The figure presents wavelet-based Shannon TE for 60-days rolling window. Warmer colours indicate stronger information transfer, while masked regions denote statistically significant TE values (p < 0.05). The lower panels show rolling TE for both directions of information flow, highlighting periods of market leadership and feedback effects.

4.5. Price Discovery Under Low and High Volatility Regimes

The rolling-window approach captures continuous time variation in price discovery but does not explicitly account for structural shifts. To address this, the study employs a Markov-switching framework to analyze price discovery across low- and high-volatility regimes, identified using the Markov-switching model. By explicitly modelling regime shifts, the analysis uncovers how the direction and strength of information transmission between futures and spot markets change across market states, thereby offering a nuanced perspective on the conditional behaviour of price discovery.

The results presented in Table 4 indicate pronounced regime heterogeneity in both persistence and information transmission. Regime 1, characterized by high persistence and longer durations, reflects stable market conditions with weak or mixed price discovery. In contrast, Regime 2 is short-lived and less persistent, capturing episodes of market stress where information transmission intensifies.

Table 4.

Regime-dependent Price Discovery.

Commodity	Regime	State Persistence	Duration	F-S	p Value	S-F	p Value
Aluminium LME	Regime 1	0.93	13.88	−0.09	0.54	0.12	0.42
Aluminium LME	Regime 2	0.53	2.13	−0.15	0.00	−0.13	0.11
Aluminium MCX	Regime 1	0.93	14.60	0.14	0.01	−0.09	0.01
Aluminium MCX	Regime 2	0.78	4.49	−0.21	0.00	−0.09	0.06
Aluminium NYMEX	Regime 1	0.967	30.47	0.043	0.16	1.167	0.243
Aluminium NYMEX	Regime 2	0.98	49.49	−0.024	0.425	−0.062	0.904
Aluminium SHFE	Regime 1	0.93	14.48	0.08	0.69	0.23	0.25
Aluminium SHFE	Regime 2	0.83	5.79	−0.17	0.15	0.46	0.00
Copper LME	Regime 1	0.97	30.59	0.04	0.07	−0.03	0.21
Copper LME	Regime 2	0.50	2.02	0.90	0.00	0.02	0.74
Copper MCX	Regime 1	0.91	10.62	0.07	0.00	−0.12	0.21
Copper MCX	Regime 2	0.76	4.11	−0.06	0.55	0.02	0.77
Copper NYMEX	Regime 1	0.92	12.29	−0.37	0.29	0.27	0.42
Copper NYMEX	Regime 2	0.63	2.69	0.54	0.30	−0.56	0.26
Copper SHFE	Regime 1	0.90	9.57	−0.03	0.65	0.48	0.00
Copper SHFE	Regime 2	0.82	5.41	0.31	0.03	0.31	0.02

Notes: F-S denotes information flow from futures to spot markets, while S-F denotes information flow from spot to futures markets. Regime 1 reflects relatively stable market conditions, while Regime 2 captures periods of higher market stress. State persistence represents the probability of remaining in the same regime, and duration indicates the expected duration of each regime. p value indicates statistical significance. LME: London Metal Exchange; MCX: Multi Commodity Exchange; NYMEX: New York Mercantile Exchange; SHFE: Shanghai Futures Exchange.

A consistent pattern emerges in which futures markets lead price discovery during volatile regimes, particularly on the LME and MCX, while in stable regimes, relationships are either bidirectional or insignificant. However, this pattern is not uniform: SHFE exhibits spot-led or bidirectional dynamics, and NYMEX shows limited evidence of integration, highlighting exchange-specific structural differences. The findings demonstrate that price discovery is inherently regime-dependent, with efficiency strengthening under volatility. This provides strong support for the AMH, emphasizing the time-varying nature of market efficiency across commodities and trading venues.

4.6. Financialization Impact on Market Efficiency Through Speculative Activity

The conceptual framework in Figure 1 posits that commodity financialization affects market efficiency by driving speculative trading by financial investors. To empirically examine this channel, the present study incorporates the speculative ratio (SR) as a proxy for speculative activity within the MS-VAR framework, allowing the impact of speculation on information transmission to vary across regimes. The SR is calculated as the ratio of trading volume to open interest (SR = Volume/Open Interest). This measure captures the extent of speculative trading activity in the futures market, with higher values indicating a relatively greater presence of speculative trades than hedging positions.

Table 5 presents the regime-dependent effects of speculative activity on market efficiency across exchanges. It is important to note that the SR has been standardized; therefore, negative values do not imply negative speculation but rather indicate levels below the sample mean. A clear pattern emerges wherein Regime 2 is associated with relatively higher speculative activity, while Regime 1 corresponds to lower-than-average speculation levels. Regime 1 is generally more persistent and longer-lasting, reflecting relatively stable market conditions with lower speculative intensity, whereas Regime 2 is comparatively shorter and characterized by elevated speculative activity. The impact of speculation on information transmission varies across regimes and markets. In several cases (e.g., Aluminium LME, MCX and SHFE), futures-to-spot relationships strengthen and become statistically significant in Regime 2, suggesting that increased speculative participation enhances price discovery. This indicates that speculative participation increases market liquidity and trading activity, facilitating faster incorporation of information into prices and strengthening price discovery. However, this effect is not uniform; for Aluminium NYMEX and certain copper markets, causality remains weak or insignificant in both regimes, indicating limited improvements in efficiency despite the level of speculation. The findings suggest that financialization, proxied by the SR, exerts a heterogeneous influence on market efficiency, supporting the view that market efficiency evolves over time and across market conditions.

Table 5.

Regime-dependent Impact of Speculative Activity on Market Efficiency.

Commodity	Regime	Persistence	Duration	SR	F-S	S-F
Aluminium LME	1	92	11.03	−0.232	0.734 (0.37)	0.032 (0.82)
Aluminium LME	2	60	2.64	1.178	0.039 (0.03)	−0.16 (0.04)
Aluminium MCX	1	0.66	2.93	−0.16	0.077 (0.082)	0.021 (0.686)
Aluminium MCX	2	0.60	2.49	0.21	0.429 (0.000)	0.145 (0.054)
Aluminium NYMEX	1	0.89	8.60	−0.04	0.023 (0.901)	0.026 (0.000)
Aluminium NYMEX	2	0.86	6.86	0.10	−0.023 (0.596)	−0.021 (0.419)
Aluminium SHFE	1	0.92	11.80	−0.16	−0.1419 (0.08)	0.5054 (0.000)
Aluminium SHFE	2	0.80	4.81	0.43	0.0756 (0.417)	0.0683 (0.162)
Copper LME	1	0.91	10.68	−0.21	−0.1896 (0.860)	0.1526 (0.892)
Copper LME	2	0.76	4.24	1.24	0.1715 (0.375)	−0.0756 (0.636)
Copper MCX	1	0.74	3.79	−0.15	−0.2367 (0.005)	−0.0009 (0.869)
Copper MCX	2	0.90	10.23	0.04	0.0005 (0.895)	0.0053 (0.904)
Copper NYMEX	1	0.8947	9.50	−0.15	−0.4411 (0.145)	0.0390 (0.882)
Copper NYMEX	2	0.667	3	0.68	0.3461 (0.145)	−0.2293 (0.882)
Copper SHFE	1	0.90	10.51	−0.17	−0.0379 (0.768)	0.5616 (0.000)
Copper SHFE	2	0.77	0.77	0.53	0.1714 (0.001)	0.4399 (0.000)

Notes: F-S denotes information flow from futures to spot markets, while S-F denotes information flow from spot to futures markets. Values in parentheses denote p values. Regime 1 reflects lower speculative activity, whereas Regime 2 represents relatively higher speculative activity. Persistence represents the probability of remaining in the same regime, and duration indicates the expected duration of each regime. LME: London Metal Exchange; MCX: Multi Commodity Exchange; NYMEX: New York Mercantile Exchange; SHFE: Shanghai Futures Exchange.

4.7. Robustness Check

The TVP-VAR model was used to further confirm that market efficiency is not constant but evolves, supporting the AMH. The results presented in Figure 5 show that aluminium and copper market efficiency varies across exchanges and over time, with heightened fluctuations, especially during global disruptions like the COVID-19 pandemic and the Russia–Ukraine conflict, suggesting sensitivity to external shocks.

Figure 5.

Note: The left panel shows the time-varying impact of futures returns on spot returns, while the right panel shows the effect of spot returns on futures returns. The dashed red line represents the zero benchmark, indicating no information transmission. Coefficients above zero imply positive information flow from the leading market, while values below zero indicate weaker or inverse transmission. Changes in the coefficients over time reflect the evolving role of spot and futures markets in the price discovery process.

4.8. Discussion

The ensuing insights outline key findings concerning the informational relationships between the spot and futures markets for base metal commodity futures across different exchanges. We demonstrate divergent IS and CS results, often caused by high residual correlation, which complicates interpretation, as noted by Baillie et al. (2002). To better capture the relationship, we employ TE models: Shannon entropy for normal market conditions and RTE to account for extreme tail events.

The results reveal that conclusions regarding price discovery leadership are sensitive to the modelling framework and market conditions. Under linear models, copper futures are found to lead price discovery across several exchanges, including MCX and LME. However, once non-linearity is explicitly accounted for using non-parametric approaches, this leadership weakens or disappears in normal market conditions. This divergence highlights that linear models may overstate the dominance of futures by imposing restrictive assumptions that fail to capture complex, asymmetric information transmission mechanisms. In normal market conditions, clearer leadership patterns emerge. Futures markets on SHFE and NYMEX predominantly lead copper price discovery, while aluminium futures on MCX and SHFE exhibit stronger informational leadership. Our analysis validated transaction cost theory in four out of eight futures markets. According to this theory, informed traders prefer to trade in markets with lower transaction costs and where information is more efficiently reflected in prices. Futures markets, by offering lower costs, higher liquidity and greater leverage, become the preferred venue for incorporating new information. The observed leadership of futures in price discovery aligns with this theoretical perspective, reaffirming that market participants strategically choose trading venues to minimize costs and maximize informational advantages. Our findings align with Yu et al. (2022), who also support the transaction cost theory.

RTE and MS-VAR results show that futures markets play a crucial role in price discovery during extreme market conditions and high-volatility regimes. These findings suggest that price discovery is regime-dependent, reinforcing the AMH framework (Lo, 2004). According to the AMH, market efficiency is rather a context-based feature that varies over time and across markets. This is reflected in the varying efficiency of base metals futures markets over time, supporting studies such as Wong et al. (2025) and Shahid et al. (2020), who also identified temporal fluctuations in market efficiency for commodities and concluded that the commodities market exhibits the AMH rather than the EMH. In contrast to Tiwari et al. (2024), who report a concave RTE pattern, interpreted as stronger information flow during normal market conditions relative to extreme events in equity–bond markets. The present study does not observe a concave relationship between RTE and the order q for spot–futures markets. The present study does not observe a concave relationship between RTE and the order q for spot–futures markets. Instead, information flow weakens monotonically as q increases, suggesting that information transmission in commodity futures markets is more sensitive to tail events and diminishes when higher-order dynamics are emphasized. Therefore, this study reinforces the view that base metal futures markets are best understood through the lens of the AMH, in which market efficiency evolves rather than remains constant. The finding that noise in information flow is not predominant suggests that the market is primarily driven by fundamentals rather than irrational speculation or misinformation. This environment supports more rational decision-making by investors, who can rely on market signals without fear of excessive volatility or manipulation. As a result, market participants may be less prone to overreact to temporary fluctuations, reducing herd behaviour and contributing to more stable pricing. This is particularly beneficial for long-term investors and policymakers who base strategic decisions on price movements and trends.

5. Conclusion and Implications

Base metals futures have become essential tools for risk management by facilitating risk transfer. However, base metal futures have seen declining volumes worldwide over the years, raising questions about the efficiency of the futures market. Moreover, existing studies on futures–spot dynamics largely rely on parametric and linear models, despite evidence that financial market information flows are inherently non-linear (Osei & Adam, 2020). Prior research has examined information transmission and price discovery using conventional causality approaches (Gupta et al., 2018; Kantamaneni & Asi, 2023; Karmakar & Inani, 2019; Rout et al., 2024), whereas more recent studies have documented non-linear relationships in spot and futures markets (Ameur et al., 2022; Li & Chavas, 2023). In addition, studies on the AMH have primarily focused on crude oil, equity, bond and precious metal markets (Shahid et al., 2020; Tiwari et al., 2024; Wong et al., 2025). Building on this literature, our study examines the efficiency of base metal futures (aluminium and copper) across NYMEX, LME, MCX and SHFE using daily data. The study employs TE, a non-parametric model, to analyze causal relationships between spot and futures prices. While prior studies have applied TE to commodity and equity market interactions (Bekiros et al., 2017; Niu & Hu, 2021), its application to spot–futures dynamics in base metals remains limited. By incorporating RTE, the study captures tail dependencies and extreme market conditions, providing a more robust framework for analyzing complex information flows and addressing limitations of traditional models.

Our findings state that the futures market leads the spot market in price discovery, providing empirical support for the transaction cost theory. The application of RTE, rolling-window analysis, and regime-based market efficiency confirms time-varying information flows between markets, which aligns with the AMH. Unlike the efficient market hypothesis, AMH posits that market efficiency is not static but evolves as investors adapt to changing environments. This supports the core premise of AMH, that markets alternate between periods of efficiency and inefficiency based on behavioural and structural shifts. Futures market leadership in price discovery confirms its role as a forward-looking, information-efficient platform, assuring investors and hedgers that they can rely on futures prices for risk management and strategic decisions. Furthermore, the high informational efficiency of the MCX can help to strengthen its reputation and attract greater domestic and foreign participation. Overall, the findings suggest that future studies should employ advanced techniques, such as TE, to better capture the complexity and non-linear nature of market behaviour. This supports the growing literature that applies entropy-based measures to evaluate market efficiency and information dynamics.

The study has certain limitations. First, it does not explicitly incorporate geopolitical risk using a formal geopolitical risk index. Second, financialization is proxied by the SR, treated as an endogenous variable within the MS-VAR framework, thereby limiting clear identification of its direct causal impact on market efficiency and price discovery. Future research may use participant-level trading data and treat these factors as exogenous variables to better capture the influence of financialization and external shocks on market dynamics. Future studies may also further examine the relationship between financialization and the AMH by exploring how market participants adapt to changing economic and financial conditions and how such adaptation influences market efficiency over time.

Footnotes

Acknowledgements

The authors sincerely thank the editor, Kakali Kanjilal, for the careful evaluation and continuous support throughout the review process. The authors are also grateful to the anonymous referees for their useful suggestions, which significantly improved the quality of the article. The authors further extend their gratitude to Praveen Kumar Sahoo for his valuable support throughout this study.

Authors Contribution

Yashmin Khatun: Conceptualization, methodology, data curation, formal analysis, visualization, writing – original draft, writing – review and editing.

Dushyant Mahadik: Conceptualization, supervision, validation, writing – review and editing.

Upelina Bina Murmu: Data curation, software, writing – review and editing.

Data Availability Statement

The data can be made available from the corresponding author upon request.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Ethical Declaration

The authors abide by all the ethics involved in this academic work and have not submitted it to any other journal.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

Generative Artificial Intelligence

The authors used Google Gemini to improve the readability and clarity of the manuscript.

Supplementary Material

ORCID iDs

Yashmin Khatun

Dushyant Mahadik

Upelina Bina Murmu

References

Aït-Youcef

, & Joëts

(2024). The role of index traders in the financialization of commodity markets: A behavioral finance approach. Energy Economics , 136, 107641. https://doi.org/10.1016/j.eneco.2024.107641

Ameur

H. B.

, Ftiti

, & Louhichi

(2022). Revisiting the relationship between spot and futures markets: Evidence from commodity markets and NARDL framework. Annals of Operations Research , 313(1), 171–189. https://doi.org/10.1007/s10479-021-04172-3

Baillie

R. T.

, Booth

G. G.

, Tse

, & Zabotina

(2002). Price discovery and common factor models. Journal of Financial Markets , 5(3), 309–321. https://doi.org/10.1016/s1386-4181(02)00027-7

Bekiros

, Nguyen

D. K.

, Junior

L. S.

, & Uddin

G. S.

(2017). Information diffusion, cluster formation and entropy-based network dynamics in equity and commodity markets. European Journal of Operational Research , 256(3), 945–961. https://doi.org/10.1016/j.ejor.2016.06.052

Bohl

M. T.

, Irwin

S. H.

, Pütz

, & Sulewski

(2023). The impact of financialization on the efficiency of commodity futures markets. Journal of Commodity Markets , 31. https://doi.org/10.1016/j.jcomm.2023.100330

Bohl

M. T.

, Pütz

, & Sulewski

(2021). Speculation and the informational efficiency of commodity futures markets. Journal of Commodity Markets , 23, 100159. https://doi.org/10.1016/j.jcomm.2020.100159

Brouty

, & Garcin

(2023). A statistical test of market efficiency based on information theory. Quantitative Finance , 23(6), 1003–1018. https://doi.org/10.1080/14697688.2023.2211108

Çağlı

E. Ç.

, Taşkın

, & Mandacı

P. E.

(2019). The short- and long-run efficiency of energy, precious metals, and base metals markets: Evidence from the exponential smooth transition autoregressive models. Energy Economics , 84, 104540. https://doi.org/10.1016/j.eneco.2019.104540

Chen

, & Tongurai

(2022). Spillovers and interdependency across base metals: Evidence from China’s futures and spot markets. Resources Policy , 75, 102479. https://doi.org/10.1016/j.resourpol.2021.102479

10.

Chincarini

L. B.

, & Moneta

(2021). The challenges of oil investing: Contango and the financialization of commodities. Energy Economics , 102, 105443. https://doi.org/10.1016/j.eneco.2021.105443

11.

Dash

, Jena

S. K.

, Tiwari

A. K.

, & Kumar

(2025). World energy futures market efficiency and its determinants: Evidence from a white-noise test based on a block-wise wild bootstrap approach. Applied Economics , 57(53), 9019–9033. https://doi.org/10.1080/00036846.2024.2405660

12.

Dergiades

, Madlener

, & Christofidou

(2018). The nexus between natural gas spot and futures prices at NYMEX: do weather shocks and non-linear causality in low frequencies matter?. The Journal of Economic Asymmetries , 18, e00100. https://doi.org/10.1016/j.jeca.2018.e00100

13.

Fama

E. F.

(1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance , 25(2), 383–417. https://doi.org/10.2307/2325486

14.

Fernandez

(2010). Commodity futures and market efficiency: A fractional integrated approach. Resources Policy , 35(4), 276–282. https://doi.org/10.1016/j.resourpol.2010.07.003

15.

Fernandez

(2016). Futures markets and fundamentals of base metals. International Review of Financial Analysis , 45, 215–229. https://doi.org/10.1016/j.irfa.2016.03.014

16.

Figuerola-Ferretti

, & Gilbert

C. L.

(2005). Price discovery in the aluminium market. Journal of Futures Markets , 25(10), 967–988. https://doi.org/10.1002/fut.20173

17.

Fung

, Liu

Q. W.

, & Tse

(2010). The information flow and market efficiency between the U.S. and Chinese aluminium and copper futures markets. The Journal of Futures Markets , 30(12), 1192–1209. https://doi.org/10.1002/fut.20474

18.

Goldstein

, & Yang

(2022). Commodity financialization and information transmission. The Journal of Finance , 77(5), 2613–2667. https://doi.org/10.1111/jofi.13165

19.

Guo

, Yao

, Cheng

, & Zhu

(2020). China’s copper futures market efficiency analysis: Based on nonlinear Granger causality and multifractal methods. Resources Policy , 68, 101716. https://doi.org/10.1016/j.resourpol.2020.101716

20.

Gupta

S. K.

, Choudhary

, & Agarwal

D. R.

(2018). An empirical analysis of market efficiency and price discovery in the Indian commodity market. Global Business Review , 19(3), 771–789. https://doi.org/10.1177/0972150917713882

21.

Hasbrouck

(1995). One security, many markets: Determining the contributions to price discovery. The Journal of Finance , 50(4), 1175–1199. https://doi.org/10.1111/j.1540-6261.1995.tb04054.x

22.

, & Lee

(2024). New evidence on crude oil market efficiency. Economic Inquiry , 62(2), 892–916. https://doi.org/10.1111/ecin.13189

23.

Islam

K. U.

, Lone

U. M.

, Gulam

Y. A.

, & Bhat

S. A.

(2025). Dynamic linkages and temporal relationships between spot and future index prices: Empirical evidence from India using non-linear GARCH–BEKK. Asia-Pacific Financial Markets , 32(2), 609–630. https://doi.org/10.1007/s10690-024-09464-9

24.

Jhunjhunwala

, & Suresh

(2020). Commodity and stock market interlinkages: Opportunities and challenges for investors in Indian market. Global Business Review , 25(2_suppl), S42–S58. https://doi.org/10.1177/0972150920946413

25.

, Bouri

, Roubaud

, & Kristoufek

(2019). Information interdependence among energy, cryptocurrency and major commodity markets. Energy Economics , 81, 1042–1055. https://doi.org/10.1016/j.eneco.2019.06.005

26.

Jizba

, Kleinert

, & Shefaat

(2012). Rényi’s information transfer between financial time series. Physica A: Statistical Mechanics and Its Applications , 391(10), 2971–2989. https://doi.org/10.1016/j.physa.2011.12.064

27.

Kang

, Tang

, & Wang

(2023). Financialization of commodity markets ten years later. Journal of Commodity Markets , 30, 100313. https://doi.org/10.1016/j.jcomm.2023.100313

28.

Kantamaneni

H. D.

, & Asi

V. R.

(2023). Market efficiency of commodity derivatives with reference to nonagricultural commodities. Asia-Pacific Financial Markets , 30(1), 247–258. https://doi.org/10.1007/s10690-023-09400-3

29.

Karmakar

, & Inani

S. K.

(2019). Information share and its predictability in the Indian stock market. Journal of Futures Markets , 39(10), 1322–1343. https://doi.org/10.1002/fut.22041

30.

Kenourgios

, & Samitas

(2004). Testing efficiency of the copper futures market: New evidence from London Metal Exchange. Global Business and Economics Review , 261–271. https://ssrn.com/abstract=869390

31.

Kia

, Liu

, Li

, Song

, & Xu

(2026). Price discovery in Bitcoin ETF market. Financial Review , 61(2), 435–449. https://doi.org/10.1111/fire.70026

32.

, & Chavas

(2023). A dynamic analysis of the distribution of commodity futures and spot prices. American Journal of Agricultural Economics , 105(1), 122–143. https://doi.org/10.1111/ajae.12309

33.

, & Xiong

(2024). Is China’s new live hog futures market efficient? Evidence from an analysis of market quality, price discovery and hedging effectiveness. Australian Journal of Agricultural and Resource Economics , 68(1), 186–205. https://doi.org/10.1111/1467-8489.12542

34.

Liu

, & Su

(2019). The dynamic causality between gold and silver prices in the Chinese market: A rolling window bootstrap approach. Finance Research Letters , 28, 101–106. https://doi.org/10.1016/j.frl.2018.04.007

35.

A. W.

(2004). The adaptive markets hypothesis: Market efficiency from an evolutionary perspective. Journal of Portfolio Management , 30, 15–29. https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID602222_code17399.pdf?abstractid=602222&mirid=1

36.

Marschinski

, & Kantz

(2002). Analysing the information flow between financial time series. European Physical Journal B—Condensed Matter and Complex Systems , 30(2), 275–281. https://doi.org/10.1140/epjb/e2002-00379-2

37.

Niu

, & Hu

(2021). Information transmission and entropy-based network between the Chinese stock market and the commodity futures market. Resources Policy , 74, 102294. https://doi.org/10.1016/j.resourpol.2021.102294

38.

Osei

P. M.

, & Adam

A. M.

(2020). Quantifying the information flow between Ghana stock market index and its constituents using transfer entropy. Mathematical Problems in Engineering , 2020, 1–10. https://doi.org/10.1155/2020/6183421

39.

Qian

, Jiang

, & Liu

(2025). Factor momentum in commodity futures markets. Journal of Futures Markets , 45(11), 1934–1969. https://doi.org/10.1002/fut.70022

40.

Robertson

, & Zhang

(2025). Price discovery in bitcoin spot and futures markets. Journal of International Money and Finance , 159, 103415. https://doi.org/10.1016/j.jimonfin.2025.103415

41.

Rout

B. S.

, Das

N. M.

, & Rao

K. C.

(2019). Volatility spillover effect in commodity derivatives market: Empirical evidence through generalised impulse response function. Vision , 23(4), 374–396. https://doi.org/10.1177/0972262919850916

42.

Rout

B. S.

, Das

N. M.

, & Rao

K. C.

(2024). Does commodity derivatives function effectively? A lengthy discussion. IIM Kozhikode Society & Management Review , 1–12. https://doi.org/10.1177/2277975220985746

43.

Sahoo

, & Kumar

(2009). Efficiency and futures trading-price nexus in Indian commodity futures markets. Global Business Review , 10(2), 187–201. https://doi.org/10.1177/097215090901000204

44.

Saji

T. G.

, & Paul

(2026). Forecasting high-frequency currency tail risks with EVT and technical indicators across pandemic phases. Cogent Economics & Finance , 14(1), 2602346. https://doi.org/10.1080/23322039.2025.2602346

45.

Samal

(2024). Market efficiency of base metal futures in India: An empirical evidence. The Indian Economic Journal , 72(2), 1–23. https://doi.org/10.1177/00194662241238594

46.

Schreiber

(2000). Measuring information transfer. Physical Review Letters , 85(2), 461–464. https://doi.org/10.1103/physrevlett.85.461

47.

Shahid

M. N.

, Jehanzeb

, Abbas

, Zubair

, & Akbar

M. A. H.

(2020). Predictability of precious metals and adaptive market hypothesis. International Journal of Emerging Markets , 15(5), 1011–1027. https://doi.org/10.1108/ijoem-07-2018-0404

48.

Shannon

C. E.

(1948). A mathematical theory of communication. Bell System Technical Journal , 27(3), 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x

49.

Sharma

, & Karmakar

(2024). Asymptotic dependence and its impact on hedging effectiveness: An examination of stock, currency, and commodity futures. Journal of Futures Markets , 44(11), 1750–1786. https://doi.org/10.1002/fut.22546

50.

Tang

C. F.

, & Abosedra

(2016). Tourism and growth in Lebanon: New evidence from bootstrap simulation and rolling causality approaches. Empirical Economics , 50(2), 679–696. https://doi.org/10.1007/s00181-015-0944-9

51.

Thenmozhi

, & Thomas

S. M.

(2007). Price discovery and volatility spillover in spot and futures markets. Indian Journal of Capital Market . https://doi.org/10.2139/ssrn.1009590

52.

Tiwari

A. K.

, Jena

S. K.

, Abakah

E. J. A.

, & Yoon

(2024). Does the dynamics between government bond and equity markets validate the adaptive market hypothesis? Evidence from transfer entropy. Applied Economics , 56(2), 186–201. https://doi.org/10.1080/00036846.2023.2166896

53.

Wong

, Lv

, Espinosa

, & Vieito

J. P.

(2025). The crude oil spot and futures prices dynamics: Cointegration, linear and nonlinear causality. Studies in Economics and Finance , 42(3), 532–552. https://doi.org/10.1108/sef-12-2023-0738

54.

Xiong

, & Li

(2024). A tale of two contracts: Was the SHFE copper futures market disrupted by the listing of INE bonded copper futures? Journal of Futures Markets , 44(2), 281–301. https://doi.org/10.1002/fut.22473

55.

(2019). Price dynamics in corn cash and futures markets: Cointegration, causality, and forecasting through a rolling window approach. Financial Markets and Portfolio Management , 33(2), 155–181. https://doi.org/10.1007/s11408-019-00330-7

56.

, Pan

, Wang

, & Li

(2019). Dynamic price discovery process of Chinese agricultural futures markets: An empirical study based on the rolling window approach. Journal of Agricultural and Applied Economics , 51(04), 664–681. https://doi.org/10.1017/aae.2019.23

57.

, Yang

, & Webb

R. I.

(2022). Price discovery in China’s crude oil futures markets: An emerging Asian benchmark? The Journal of Futures Markets , 43(3), 297–324. https://doi.org/10.1002/fut.22384

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.03 MB