# Does Indian Commodity Futures Markets Exhibit Price Discovery? An Empirical Analysis

Authors: Upananda Pani; Ştefan Cristian Gherghina; Mário Nuno Mata; Joaquim António Ferrão; Pedro Neves Mata
Journal: Discrete Dynamics in Nature and Society
 (2022)

---

## Abstract

Price discovery function analyses the dynamics of futures and spot price behavior in an asset’s intertemporal dimensions. The present study examines the price discovery function of the bullion, metal, and energy commodity futures and spot prices through the Granger causality and Johansen–Juselius cointegration tests. The Granger causality test results show bidirectional causality between the spot and futures returns for gold, silver, aluminum, lead, nickel, and zinc. The Johansen cointegration test shows that spot and futures prices are in the long-run equilibrium path for silver, aluminum, lead, nickel, zinc, crude oil, and natural gas. The vector error correction model results suggest that both the spot and futures markets are equally efficient in price discovery for the nickel. The spot market leads the futures market in price discovery for copper and zinc. However, the futures market leads the spot market in price discovery for silver, aluminum, and lead. The findings of the study suggest the market participants for implementing hedging and arbitrage strategies. It also helps the market regulators to examine the stability of these rapidly growing commodity futures markets in India.


---

## Body

## 1. Introduction

Commodities such as agriculture, metal, and energy are valuable to producers, processors, consumers, lenders, and brokers. Commodities trade on both spot and derivative markets across world commodity derivative markets [1]. Commodity derivative markets include trading of forwards and futures contracts, which derive its values from the market’s spot commodities. As a welfare raising mechanism, an efficient commodity futures market plays a vital role in managing price risk uncertainty contextual to the primary commodities [2]. In an open economy, commodity futures markets hold pervasive importance in discovering a reference price for the producers and trade functionaries by reducing price volatility in the commodity prices and uncertain production decisions [3, 4]. Apart from price discovery, Li and Xiong [5] argued that the futures market is a significant instrument for risk management since it provides financial gains such as dissemination of information, and efficient resource allocation. Eventually, the spot price is affected by fundamental factors such as demand and supply, market structure, and government policies. In contrast, the futures price is driven by hedgers, speculators, traders, and other market participants. The study of price behavior in commodity futures markets provides a better analytical perspective towards futures contracts’ pricing and on how futures market prices affect the commodities’ spot price over time.Interest in the Indian commodity futures markets is showing an increasing trend over the years. Commodity futures emerges as an attractive investment alternative to the security markets and is also recognized as an increasingly popular vehicle to hedge investments [6]. The existing literature on price discovery and market efficiency in Indian commodity futures markets supports an efficient functioning commodity futures market’s economic significance [7–9]. In developed countries, earlier studies emphasized the economic role and function of the commodity futures markets. The researchers’ issues drawn considerable attention from the researchers that include intertemporal price behavior, hedging effectiveness, and basis relationship [10, 11].However, in developing countries, futures markets are subject to higher government control, and reforms are relatively new. There is a gradual shift from an intervention approach to a market-based system in government policies. So, the commodity futures markets’ economic role attracted the debate on these markets’ economic benefits, such as price discovery and hedging [12]. Given the dynamic, economic, and institutional factors pertinent to the emerging economy, it is evident to expect a significant difference in the dynamics of commodity price behavior in these markets compared to that in a developed economy.In the context of India, following the reform in the commodity derivative market since 2003, the commodity futures trading for agriculture, metal, and bullion commodities is growing significantly across major commodity exchanges [7, 13, 14]. However, the commodity futures market development’s role in minimizing price risk uncertainty and economic efficiency in the spot markets needs to be studied. It is essential to explore the issues that explain the dynamics of Indian commodity futures markets’ pricing behavior.As the futures markets play a significant role in managing price risk and serves the price discovery role for the spot market in the economy, there is a need to look at the dynamics of the futures market’s price behavior. In this context, a question arises about how does the futures prices behave?, how to interpret the information it conveys to the market?, and whether futures contracts are effective in reducing price risk? These issues are more pertinent for assessing the performance of the commodity futures market in India. The present study thus attempts to determine the price discovery role of the commodities traded in newly established futures exchanges. Prior studies for India were focused on spot and futures agricultural commodity markets [15–20], gold exchange traded funds [21], metals [22], spot and futures index [23, 24], daily futures, and spot closing prices for various commodities [25–27], both commodities and indices [28]. As compared with earlier literature, the novelty of the current study consists in the fact that three commodity groups are covered, namely, bullion (gold, and silver), metal (aluminum, copper, lead, and zinc), and energy (crude oil and natural gas) over a longer period, respectively, (2006–2018).The remainder of this paper is organized as follows. Section2 provides an overview of Indian commodity derivative markets. Section 3 presents the review of earlier literature. Section 4 is focused on empirical techniques. Section 5 exhibits the econometric outcomes. The last section concludes the manuscript and provides policy implications.


## 2. An Overview of Commodity Derivative Markets in India

The Government of India (GoI) brought various regulations to increase the markets’ financialization for multiple commodities. The primary reasons include shifting the price fluctuation risk through hedging and performing the price discovery function and price reference for the spot market [29, 30]. Futures markets serve risk transference and price discovery functions to the economy [31–35]. The presence of speculators facilitates a risk transference function by buying a futures contract from hedgers. The price discovery function implies the use of futures prices on the price formation and transactions in the spot market [31, 33, 36]. So, both price discovery and risk transfer are crucial to justify the futures markets’ economic benefit. However, the above features of a futures market are only theoretical. It is necessary to empirically validate these economic functions for evaluating the market performance to meet the objective of an efficient market structure for the commodity market. Alternatively, if futures markets are indeed performing the economic role as mentioned earlier satisfactorily, then there is a strong case for introducing new futures markets for other commodities.Since the year 1875, commodity futures trading came into existence in India. Still, the market was said to be in hibernation for five decades resulting from strict government control (Kabra, 2007). In the year 2003–04, massive developments took place in the commodity futures market. On April 1, 2003, the government’s notification led to the withdrawal of the previous announcements, which restricted futures trading of large quantities in India. Furthermore, a notification came in May 2003, canceling restrictions on nontransferable specific delivery forward contracts. Thus, GoI reduced the restriction in the futures market in expectation of a healthy market institution and efficient market structure. GoI further granted recognition to National Multi-Commodity Exchange of India Limited (NMCEIL), Ahmedabad, in 2002, Multi Commodity Exchange (MCX), Mumbai, and National Commodity and Derivatives Exchange Limited (NCDEX), Mumbai, in the year 2003, followed by Indian Commodity Exchange Limited (ICEXL), Gurgaon, in 2009. The establishment of national-level commodity exchanges resulted in a manifold increase in futures trading. The total turnover of futures trading increased from Rs. 1,294 billion to Rs. 60,070 billion from the year 2003–04 to 2017–18, whereas the total turnover to a gross domestic product increased from 4.6% in 2003–04 to 142.15% in 2017–18 [37, 38]. The developments in commodity futures markets resulted in the exponential growth of the commodity futures segment in the Indian economy. In recent years, commodity futures markets drew attention from the researchers regarding issues such as market efficiency, price discovery, risk management, international linkage, and other matters related to Indian commodity derivative markets [7–9, 14, 39–46].


## 3. Prior Literature on the Relationship between Futures and Spot Prices

The previous studies [31, 36, 47] emphasized the role of futures markets in price discovery in spot markets. Price discovery also predicts the expected futures spot prices and using the futures prices as a reference price in the spot market. It also helps in finding a reference price for the spot market and helps in identifying the feedback process of information of futures price and spot price. Futures prices shows the expected spot prices [48]. The futures market performs a price discovery function that depends upon the intertemporal relationship between spot and futures prices. Price discovery process reveals us whether futures (spot) market will lead to spot (future) market if all the available information passes on to futures (spot) price and then in spot (future) prices. When all available information is fully and instantaneously utilized in an efficient market to determine the market price, then futures price moves closely with its corresponding price in the spot market with no lag or lead in price movement from one market to another. If there is no difference in each of these markets, then both spot and futures market will react instantly without any lead or lag to the flow of information. Since futures and spot markets represent the same commodity, their prices should exhibit a similar reaction to a given information or event, a process facilitated by arbitrage [49]. A review of previous literature regarding price discovery in commodity futures markets is revealed in Table 1.Table 1
Summary of earlier studies regarding price discovery in commodity futures markets.
Author(s)PeriodVariablesEconometric methodsEmpirical outcomesIndian commodity marketsVijayakumar [19]January 2017–March 2020CardamomJohansen cointegration, vector error correction model, Granger causality, and regression with dummy variablesCardamom e-auction prices exhibit a negative association with cardamom futures but a positive relation with spot pricesPradhan, Hall, and Toit [28]2009–2020Commodities (aluminum, copper, crude oil, gold, nickel, and silver) and indices (agriculture, livestock, and precious metals)ARDL bounds testingLong-run unidirectional causality from spot to futures prices for aluminum, copper, and silver but short-run bidirectional, unidirectional, and neutrality between spot and futures pricesRout, Das, and Rao [16]January 2010-December 2015Chana, chilli, jeera, soya bean, and turmeric.Causality test, error correction model, EGARCH, and parametric VaRVolatility spreads from the spot market to the futures marketNair [22]January 2008-December 2019Aluminium, Copper, Nickel, and ZincJohansen test, error correction model, and Granger causalityMetals’ futures prices are heavily weighted in predicting futures spot market pricesNair [18]January 2004–December 2019Pepper, cardamom, and natural rubberCointegration-ECM-GARCH frameworkPrice discovery in commodity futures markets is efficientMohanty and Mishra [17]October 2015–March 2016Castor seed, cotton oil cake, rape mustard seed, soybean, refined soya oil, crude palm oil, jeera, chana (chickpea), and turmericVariance ratio testsAgricultural commodity futures markets in India are inefficient in the short term both before and after mergerManogna and Mishra [15]2010–2020Oil seeds (cotton seed, castor seed, soybean seed, rape mustard seed), spices (turmeric, jeera coriander), and grains (guar seed, chana)Granger causality, vector error correction model (VECM) and exponential generalized autoregressive conditional heteroskedasticity (EGARCH)Price discovery exists in all of the commodities studied, with the futures market outperforming the spot market in six of them: soybean seed, coriander, turmeric, castor seed, guar seed, and chanaKaur and Singh [21]2007–2016Gold exchange traded fundsJohansen test of cointegration, fully modified ordinary least squares, Toda-Yamamoto test of causalitySpot and futures price movements have been found to lead those of exchange traded fundsJena, Tiwari, Hammoudeh, and Roubaud [27]2005–2017Bullion commodities (gold and silver), and energy commodities (Brent crude oil and natural gas)Causality-in-quantiles testBecause of its informational efficiency, the foreseeability of the futures market is high in the normal market and declines when the spot market enters severe bearish and bullish situationsBhaumik, Karanasos, and Kartsaklas [24]1995–2007NSE indexBivariate ARFI-FIGARCHThe integration of futures trading lessens spot variabilityInoue and Hamori [23]January 2006–March 2011The spot index (MCXSCOMDEX) and futures index (MCXCOMDEX)Dynamic ordinary least squares (DOLS) and fully modified ordinary least squares (FMOLS)The futures market for commodities appears to be efficientJoseph, Sisodia, and Tiwari [25]January 2008–December 2012Gold, silver, crude oil, natural gas, aluminium, copper, chana, and soybeanGranger causality test and causality analysis in the frequency domainAlmost all of the commodities selected have one-way relationships from futures to spotMahalik, Acharya, and Babu [50]June 2005–December 2008Agriculture futures price index (LAGRIFP), energy futures price index (LENERGYFP), and aggregate commodity index (LCOMDEXFP)Vector error correction model (VECM) and bivariate exponential Garch model (EGARCH)Futures commodity markets exert a leading role and offer effective price discovery in the spot commodity marketAli and Gupta [20]2004–2007Wheat, rice, maize, chickpea, black lentil, red lentil, guar seed, pepper, cashew, castor seed, soybean, and sugarJohansen cointegration analysis, and Granger causalityMost agricultural commodities exhibit a long-term connection among futures and spot pricesWorldwide commodity marketsJian, Li, and Zhu [51]April 2015–April 2018CSI300, SSE50, and CSI500Skewness-dependent multivariate conditional autoregressive value at risk model (SDMV-CAViaR)Severe risk overflows in both directions among the Chinese stock index futures and spot marketsChen and Tongurai [52]April 2015–March 2020Copper, aluminium, zinc, lead, nickel, and tinForecast error variance decompositionChinese futures markets for base metals tend to produce more spillover effects than spot marketsYu, Ding, Sun, Gao, Jia, Wang, and Guo [53]July 2003–December 2019Shanghai metal exchange copper spot prices, COMEX copper futures prices, LME copper futures prices, and Shanghai futures exchange copper futures pricesWavelet decompositionThe futures markets in New York and London are more associated with the Chinese spot market than the Shanghai futures marketAusloos, Zhang, and Dhesi [54]2007–2013CSI-300 index (China-Shanghai-Shenzhen-300-Stock index) and CSI-300 index futures (CSI-300-IF)TGARCH, Granger causality, and regression analysisTwo-way Granger causality among futures and spot market in ChinaGo and Lau [55]January 2000–July 2016Crude palm oil spot and futures prices in Malaysian currencyVariance ratio testsDuring the bear market time span, spot and futures prices are strongly linkedKirkulak-Uludag and Lkhamazhapov [56]2008–2013Russian spot and three-month futures gold pricesCorrected dynamic conditional correlation modelThe conditional correlation among spot and futures gold returns is significantly greaterSource: authors’ own work.A lead-lag relation may exist between the spot and futures markets if one market processes information faster than the other. The factors which affect the lead-lag relationship include ease of short sale, lower transaction cost, institutional arrangement, and market microstructure effect. The lead-lag characteristics of futures and spot markets illustrate how rapidly one market incorporates information relative to others [57]. These characteristics also indicate the efficiency of their functioning and the degree of integration between the two markets [58]. Traders act faster at a lower cost in the futures market than spot market resulting in a lead-lag relation between futures and spot prices [59]. Lin, Chou, and Wang [60] argued that the time-differing lead-lag connection between futures and spot markets is caused, at least to some extent, by the impact of changeable investor confidence. Corredor, Ferrer, and Santamaria [61] revealed that throughout periods of high investor sentiment, the connection between the spot and futures markets diminishes substantially.Futures trading facilitates the allocation of production and consumption over time by providing market guidance in holding inventories [48]. If the futures price for distant delivery is higher than that for early delivery, the postponement of consumption becomes attractive. Thus, a change in futures price results in a subsequent change in spot prices. Speculators prefer to hold a futures contract because they are not interested in the physical commodity per se, and a futures position can be offset easily. Furthermore, hedgers interested in the physical commodity and have storage constraints may hedge themselves by buying a futures contract. Therefore, both hedgers and speculators may react to information by transacting in futures rather than in the spot market. Consequently, futures price tends to lead the spot price. Chen, Wei, Jin, and Liu [62] found that in the energy futures markets, speculative attitude causes greater market movements than hedging sentiment. In light of the above, the issue of the causal linkage between two markets provides a clear motivation for studying the lead-lag relationship between futures and spot prices.


## 4. Data and Methodology

The present study used the spot and futures price data from the Bloomberg database. Twenty-one commodity exchanges are operating in India, among them, four exchanges, namely, MCX, NCDEX, NMCEIL, and ICEXL, are national-level commodity exchanges. The rest 17 are regional exchanges in various states to cater to local needs commodity price risk management. According to Futures Industry Association Report [63], MCX is ranked 22nd globally (ranked first among commodity exchanges of India) in terms of total contracts traded in bullion, currency, metal, and energy commodity futures in the year 2019.Table2 shows the detailed sample information of the selected commodities for the study. The study used the daily closing futures price of gold, silver, aluminum, copper, lead, nickel, zinc, crude oil, and natural gas traded at MCX. According to Table 3, MCX has the highest share of the total value of trade (from 63.53% to 86.64%) among commodity exchanges in India over the period from 2006 to 2018. Hence, futures prices of various commodity contracts are selected from MCX. The study selected commodities based on each commodity’s share in the total trade value in MCX and other exchanges. As well, MCX has the highest percentage of the total value of trade for commodities: gold, silver, aluminum, copper, lead, zinc, crude oil, and natural gas. The total value of traded contracts for these commodities’ trade was collected from the Securities and Exchange Board of India (SEBI), the market regulator for the commodity futures market. Metal commodity futures was introduced by the MCX in 2005, whereas bullions were introduced in 2003. One year gap was given in the sampling period to avoid high fluctuation in the dataset.Table 2
Sample details.
GroupCommodityObservationsStart dateEnd dateQ/BTrading unitBullionGold39966-Feb-0631-Dec-1910 gm1 kgSilver416626-May-0531-Dec-191 kg30 kgMetalAluminum39534-Jan-0631-Dec-191 kg5 tonsCopper146214-Feb-0629-Nov-191 kg1 mtLead35252-Jul-0731-Dec-191 kg5 tonsNickel36738-Feb-0731-Dec-191 kg250 kgZinc38642-May-0631-Dec-191 kg5 tonsEnergyCrude oil39902-Jan-0618-Dec-191 barrel100 barrelNatural gas382720-Oct-0631-Dec-19mmbtu1250 mmbtuNote. (i) Q/B and T.U. refers to quotation per base value and trading unit. (ii) Trading unit for gold, silver, and nickel is expressed in kilogram, whereas for Aluminum, lead, and zinc, it is in tons. Trading unit of copper refers to million tons. Similarly, for crude oil and natural gas, these are barrel and mmbtu, respectively.Table 3
Commodity wise total value of trade (%) in Multi Commodity Exchange Limited (MCX).
GroupCommodity20062010201520172019BullionGold88.8394.58100.0099.4097.15Silver87.2897.4898.7599.79100.00MetalAluminum75.83100.0091.9785.2289.37Copper99.98100.00100.0099.3199.80Lead0.00100.0099.2198.0696.73Zinc99.62100.0099.7297.0097.65EnergyCrude oil100.00100.0098.4699.7290.16Natural gas100.00100.00100.00100.00100.00Source: compiled from Fortnightly Market Review, Forward Market Commission and SEBI, India (2005–2019).The futures data include near month series of the daily closing price for the selected commodities. Continuous futures price series data for the selected commodities are collected from the Bloomberg database. Return series is defined as the first difference of natural logarithmic spot priceSt and the futures price Ft at the level. These are mentioned as follows:(1)ΔSt=Rst=lnSt−lnSt−1,ΔFt=Rft=lnFt−lnFt−1.The relationship between spot and futures prices can be explained through the cost-of-carry model and the efficient market hypothesis [64]. If spot price St and futures price Ft series are integrated or I (1), we can estimate the Johansen test of multivariate cointegration test [65, 66] for establishing long-run equilibrium and vector error correction model [67] for the direction of short-run causality. This can be expressed as follows:(2)Ft=β0+β1St+εft,(3)St=α0+α1St+εst,where St=LnSt and Ft=LnFt parameters are represented by α and β, and εft,εst represent the deviations from equilibrium relationship between two prices. Johansens’s method of cointegration can be explained through vector autoregressive (VAR) representation for (2) and (3).(4)Xt=A0Xt−1+A1Xt−2+AkXt−k+εt,where Xt=StFt2×1StFt′ vector represents the natural logarithm of spot and futures price, respectively; εt=εstεFt2×1 is a vector of εstεft′ error terms of St,Ft, and εst,εft∼WN0,σ2; A0=a0a02×1 represents a vector of constant, and A1=a1,11a1,12a1,21a1,222×2 represents the parameter matrix. Equation (4) can be transformed into the following forms:(5)ΔXt=A0+ΠXt−k+Γ1ΔXt−1+⋯+Γk−1ΔXt−k+1+εtΔXt=A0+ΠXt−k+∑i=1k−1ΓiΔXt−k+1+εt,where Π=∑j=1kAj−I and Γi=∑j=1iAj−I.The rankr test r=0,1,…,g−1 of Π matrix gives the number of cointegration relations between the variables. If the rank of Π matrix is 1<rankΠ<g, then Π=αg×r∗βr×g′=α11α12β11β12, β matrix gives the cointegrating parameters β1,β2, and α matrix gives the adjustment parameters α1,α2. Johansen’s method proposes trace λTracer and likelihood ratio tests for identifying and estimating the number of cointegrating vectors. The tests can be defined as follows:(6)TraceStatistics:λTracer=−T∑i=r+1nln1−λ^i.λTrace test statistics tests the null hypothesis of the number of cointegrating vector r s against the alternative hypothesis r+1.(7)Maximum Eigenvalue statistics:λMaxr,r+1=−Tln1−λ^r+1.λTrace test statistics tests the null hypothesis of the number of cointegrating vector r s against the alternative hypothesis r.A vector error correction model (VECM) exists for a set of cointegrated variables (Engle and Granger [67], which can be expressed in a bivariate case with lag 1 as follows:(8)ΔFtΔSt=δ1δ2+Γ11Γ12Γ21Γ22ΔFt−1ΔSt−1+αfαsFt−1−β2St−1+εftεst.For the futures market to error correction,αf<0, and similarly, for spot market to error correction, αs>0. αf and αs represent the coefficients of error correction term and it shows short-run adjustment factors. Error correction terms show how fast the disequlibrium error adjusts to the long-run equilibrium path.After estimating the cointegrating vector and vector error correction model, the Granger causality test [68, 69] can be used to find out the short-run causality and long-run causality between spot and futures price. The vector error correction model (VECM) in (8) can be represented in the more general form for kth order lag as follows:(9)ΔFPt=δ1+∑i=1kΓfp,iΔFPt−i+∑i=1kΓsp,iΔSPt−i+α1FPt−i−βSPt−i+εfp,(10)ΔSPt=δ1+∑i=1kΓsp,iΔSPt−i+∑i=1kΓfp,iΔFPt−i+α2FPt−i−βSPt−i+εsp.The null hypothesisΓ11Γ12Γ21Γ22ΔSt−1=00 implies that lagged terms ΔFt−1ΔSt−1 can be tested for short-run causality and with standard likelihood ratio test with χ2 distribution between spot and futures prices expressed as follows:(11)ΔFtΔSt=δ1δ2+Γ11Γ12Γ21Γ22ΔFt−1ΔSt−1+αfαsFt−1−β2St−1+εftεst.The null hypothesisH0 for (9) H0:∑ikΓsp,i=0 implies that the lagged values of ΔSP do not Granger cause ΔFP or there is no short-run causality between futures price and spot price. Similarily, in (10), the null hypothesis H0:∑ikΓfp,i=0 shows that the lagged values of ΔFP do not Granger cause ΔSP or there is no short-run casusality between spot price and futures price.


## 5. Results and Discussion

### 5.1. Descriptive Statistics

Tables4 and 5 show the descriptive statistics of the selected commodities for spot and futures returns. The average percentage return in the spot market is higher than the futures market for all the commodities. However, the futures return is negative for zinc and natural gas, which implies a downward bias of futures prices in the futures market. The standard deviation is higher in the spot market for all the commodities than that in the futures markets. It also shows that the spot market is highly volatile than the futures market. The spot return’s unconditional distributions are negatively skewed for copper, whereas such distributions of the futures return are negatively skewed for gold, silver, aluminum, and zinc. Spot return distribution is platykurtic for gold, silver, lead, and zinc. However, the spot return distribution is leptokurtic for copper, nickel, crude oil, and natural gas. Spot return for aluminum shows the mesokurtic type of distribution. Futures return distribution is leptokurtic for all the commodities except zinc. Minimum spot return varies from −6.44% (for zinc) to −66.65% (for copper), and maximum spot return varies from 13.19% (for gold) to 82.70% (for natural gas), as shown in Table 4. Similarly, minimum futures return varies from −6.33% (for copper) to −15.90% (for silver), and maximum futures return varies from 5.47% (for gold) to 22.17% (for lead), as shown in Table 5.Table 4
Descriptive statistics of selected commodities for spot return.
GroupCommodityMeanStd. DevSkewnessKurtosisMinMaxJ-B statBullionGold0.01830.01990.2761−2.3658−0.06800.131944.4369Silver0.03380.02840.2558−2.5279−0.08350.161234.8346Base metalsAluminum0.02900.02470.39150.3661−0.08220.1703758.5985Copper0.01340.0526−3.240441.2291−0.66650.25381995.4000Lead0.01980.03320.1312−1.7161−0.10950.169277.1338Nickel0.02310.03920.57781.1388−0.11590.3037918.3396Zinc0.02880.03070.4878−1.6323−0.06440.1575168.4567EnergyCrude oil0.03370.04911.96765.8151−0.09520.42515898.1310Natural gas0.07900.11162.82577.6306−0.09120.82717752.7000Table 5
Descriptive statistics of selected commodities for futures return.
GroupCommodityMeanStd. DevSkewnessKurtosisMinMaxJ-B statBullionGold0.00070.0104−0.47983.3165−0.08000.05472550.9430Silver0.00100.0153−0.87398.4257−0.15910.08809547.0380Base metalsAluminum0.00020.0146−0.76206.9756−0.15610.05876458.7260Copper0.00050.01450.54252.0853−0.06330.10601652.9410Lead0.00030.02270.89766.7044−0.11440.22184343.0010Nickel0.00000.02260.27990.1735−0.10130.1315516.9168Zinc−0.00010.0195−0.0179−1.0128−0.08610.0832235.8748EnergyCrude oil0.00040.01670.05520.4974−0.08720.1078776.1763Natural gas−0.00020.02341.04164.5081−0.08920.19173249.1260


### 5.2. Stationarity Test

Augmented Dickey–Fuller (ADF) test results are presented in Table6. The test shows that the log of spot and futures prices for level is nonstationary for all the commodities, alike prior studies [15, 16, 18–20, 22, 23, 26, 28, 50]. The null hypothesis of nonstationary is statistically not significant for both the price series in the level. However, the null hypothesis is statistically significant at 1% level of significance for both the spot and futures prices in difference. Thus, the test indicates that the difference of log spot and futures prices is integrated with order 1 for all the commodities. The result of the unit root test directs to proceed for the cointegration analysis, where the first condition, i.e., both the series, must be nonstationary in level and integrated of order one for the Johansen–Juselius (J-J) test needs to be satisfied.Table 6
Unit root test of spot and futures prices (level and difference) for the selected commodities.
GroupLevels (log)First difference (log)CommodityConstraintSpotFutureConstraintSpotFutureIntegrationBullionGoldI and T−3.01−2.90I−10.48−10.42I (1)SilverI and T−1.72−2.12I−10.67−10.22I (1)Base metalsAluminumI and T−1.85−1.81I−10.37−10.77I (1)CopperI and T−1.90−2.15None−11.54−8.49I (1)LeadI−1.67−1.79None−9.74−9.71I (1)NickelI−1.89−1.73I and T−11.26−10.84I (1)ZincI−1.22−1.16None−10.69−10.50I (1)EnergyCrude oilI and T−1.76−1.80None−12.37−10.92I (1)Natural gasI−2.20−2.05None−10.12−10.27I (1)Note. The Fuller critical values for ADF test at 1%, 5%, and 10% are -3.43, −2.86, −2.57, respectively for constant. The Fuller critical values for ADF test at 1%, 5%, and 10% are -3.96, −3.41, and −3.12, respectively for constant + time trend (denoted by I and T). The Fuller critical values for ADF test at 1%, 5%, and 10% are −2.58, −1.95, and −1.62, respectively for no constant or time trend (denoted by none).


### 5.3. Granger Causality Test

Before estimating the cointegration test in vector autoregressive (VAR) framework, the Granger causality test is conducted to know if any unidirectional or bidirectional causality relationship exists between spot and futures prices, in line with earlier research [15, 18–20, 22]. Granger causality test is estimated following the equations (10) and (11). The estimation results from the Granger causality test are presented in Table 7. The null hypothesis that spot return does not Granger cause futures return is rejected for gold, silver, aluminum, lead, nickel, zinc, and crude oil. It implies that the spot returns cause futures returns in these commodities. The null hypothesis cannot be rejected for copper and natural gas. It implies that spot return does not cause futures return for copper and natural gas. The null hypothesis that futures return does not Granger cause spot return is rejected for all the commodities. Therefore, futures return Granger causes spot returns for all the commodities. Granger causality test suggests a bidirectional causality relationship between spot and futures prices for gold, silver, aluminum, lead, nickel, zinc, and crude oil. However, futures return does not Granger cause the spot return for copper and natural gas. As the Granger test suggests bidirectional causality between spot and futures prices for most of the commodities, there is a need to explore their meaningful relationship in the long run and short run using the J-J cointegration test followed by the estimation of a dynamic VECM.Table 7
Granger causality test of spot and futures returns for the selected commodities.
GroupCommoditySpot does not Granger cause futuresFutures does not Granger cause spotF-statP-valueF-statP-valueBullionGold6.0520.001175.1140.001Silver2.1930.031140.5480.001Base metalsAluminum9.2540.00123.9130.001Copper0.3910.89262.0220.001Lead5.2350.00137.2010.001Nickel3.1350.00146.2840.001Zinc3.1640.00169.6120.001EnergyCrude oil3.5420.001116.8420.001Natural gas0.7810.59276.0210.001Note. Spot and futures represent spot return and futures return, respectively. p value (0.001) refers to the significance at 1% level.


### 5.4. Johansen and Juselius (J-J) Cointegration Analysis

Following the stationarity test results of the previous section, the J-J cointegration test is estimated for the spot and futures prices, which are integrated of order one. Identification of the cointegrating relationship among the variables is important, as the VAR model in the first difference is misspecified for the two nonstationary variables, which are cointegrated. After identifying the cointegration relationship(4), VAR will include residuals from the vectors (lagged one period) in the VECM (Engle and Granger, 1987). The J-J cointegration test is estimated by following the Johansen and Juselius (1990) method. The results are presented in Table 8.Table 8
Johansen and Juselius cointegration rank test of spot and futures prices.
GroupCommodityLag lengthMaximum trace valueMaximum eigen valueRemarkH0: rank = 0 vs H1: rank = 1H0: rank = 1 vs H1: rank = 2H0: rank = 0 vs H1: rank = 1H0: rank = 1 vs H1: rank = 2BullionGold1018.842.4414.402.44NSSilver637.223.6533.573.651Base metalsAluminum660.952.8758.082.871Copper772.453.6668.803.661Lead955.103.3751.733.371Nickel1029.774.3125.464.311Zinc851.042.8548.192.851EnergyCrude oil1023.503.6520.853.651Natural gas414.903.0811.813.08NSNote. Critical values of λtracer=0 for 1%, 5%, and 10% significance levels are 24.6, 19.96, and 17.85, respectively. Critical values of λtracer=1 for 1%, 5%, and 10% are 12.97, 9.24, and 7.25, respectively. Critical values of λMaxr=0 for 1%, 5%, and 10% are 20.2, 15.67, and 13.75, respectively. Critical values of λMaxr=1 for 1%, 5%, and 10% are 12.97, 9.27, and 7.52, respectively. AIC lag selection criteria are used for the estimation.λtrace test rejects the null hypothesis of no cointegrating vectors r=0 at 1% significance level for silver, aluminum, copper, lead, nickel, and zinc, and it also rejects the same at 5% level for crude oil. Hence, it accepts the null hypothesis of more than zero cointegrating vectors. λtrace test accepts the null of no cointegrating vector in the case of gold and natural gas. It also accepts the r≤1 cointegrating vector’s null hypothesis against the alternative hypothesis of more than one cointegrating vectors r>1 for silver, aluminum, copper, lead, nickel, and zinc. Similarly, λmax test rejects the null hypothesis of no cointegrating vectors r=0 at 1% level of significance for silver, aluminum, copper, lead, nickel, zinc, and crude oil. So, it accepts the alternative hypothesis of one cointegrating vector r=1. λmax test accepts the null hypothesis of one cointegrating vector r=1 against the null hypothesis of two cointegrating vector r=2. Both λtrace and λmax tests suggest the presence of one cointegrating vector for silver, aluminum, copper, lead, nickel, zinc, and crude oil. The tests reject the presence of any cointegrating vector for gold and natural gas. Hence, a dynamic VECM is estimated for all those commodities, where there is a presence of a cointegrating relationship between the spot and futures prices.


### 5.5. Vector Error Correction Model

Results from the estimation of VECM (8) and (9) for spot and futures prices are presented in Tables 9 and 10. Accordingly, the results are interpreted for different commodities separately.Table 9
Vector error correction model for spot price of the selected commodities.
CoefficientsSilverAluminumCopperLeadNickelZincCrude oilαs−0.01−0.06∗−0.19∗∗−0.15∗−0.07∗−0.13∗∗∗−0.02∗∗∗(−0.98)(−2.44)(−8.34)(−2.54)(−2.17)(−3.45)(−1.39)ΔSt−1−0.43∗∗∗−0.25∗∗∗−0.25∗∗∗−0.44∗∗∗−0.48∗∗∗−0.57∗∗∗−0.43∗∗∗(−14.81)(−8.08)(−9.33)(−10.34)(−11.45)(−15.68)(−14.51)ΔSt−2−0.32∗∗∗−0.19∗∗∗−0.52∗∗∗−0.42∗∗∗−0.38∗∗∗−0.52∗∗∗−0.27∗∗∗(−10.20)(−5.65)(−19.63)(−8.38)(−7.76)(−11.10)(−8.31)ΔSt−3−0.23∗∗∗−0.17∗∗∗−0.24∗∗∗−0.35∗∗∗−0.28∗∗∗−0.40∗∗∗−0.17∗∗∗(−7.09)(−4.87)(−8.05)(−6.18)(−5.19)(−8.33)(−4.97)ΔSt−4−0.16∗∗∗−0.13∗∗∗−0.30∗∗∗−0.37∗∗∗−0.33∗∗∗−0.35∗∗∗−0.05(−5.09)(−3.61)(−10.93)(−6.15)(−6.02)(−6.90)(−1.39)ΔSt−5−0.06∗−0.11∗∗−0.23∗∗∗−0.32∗∗∗−0.25∗∗∗−0.26∗∗∗−0.04(−2.26)(−2.96)(−8.71)(−5.04)(−4.35)(−5.01)(−1.16)ΔSt−6——−0.23∗∗∗−0.23∗∗∗−0.20∗∗∗−0.21∗∗∗−0.04——(−8.97)(−3.47)(−3.43)(−4.12)(−1.06)ΔSt−7———−0.18−0.15−0.21−0.17———(−2.79)(−2.58)(−4.46)(−5.05)ΔSt−8———−0.21∗∗−0.29∗∗∗—−0.12∗∗∗———(−3.25)(−5.31)—(−3.49)ΔSt−9————−0.15∗∗—−0.14∗∗∗————(−3.08)—(−4.98)ΔFt−10.68∗∗∗0.39∗∗∗0.11∗∗∗0.73∗∗∗0.75∗∗∗0.78∗∗∗0.88∗∗∗(28.59)(11.65)(17.84)(14.64)(16.80)(20.19)(26.89)ΔFt−20.31∗∗∗0.22∗∗∗0.23∗∗∗0.51∗∗∗0.52∗∗∗0.66∗∗∗0.35∗∗∗(9.59)(5.86)(3.43)(8.54)(9.51)(13.57)(8.41)ΔFt−30.28∗∗∗0.11∗∗0.57∗∗∗0.39∗∗∗0.32∗∗∗0.49∗∗∗0.22∗∗∗(8.62)(2.95)(8.28)(5.99)(5.35)(8.97)(5.06)ΔFt−40.21∗∗∗0.17∗∗∗0.17∗0.37∗∗∗0.30∗∗∗0.39∗∗∗0.14∗∗∗(6.35)(4.44)(2.49)(5.28)(4.73)(6.75)(3.31)ΔFt−50.12∗∗∗0.09∗∗∗0.35∗0.33∗∗∗0.31∗∗∗0.28∗∗∗0.03(3.84)(2.21)(5.12)(4.47)(4.74)(4.69)(0.71)ΔFt−6——0.16∗0.21∗∗0.24∗∗∗0.22∗∗∗0.07——(2.31)(2.74)(3.66)(3.68)(1.64)ΔFt−7———0.15∗0.16∗0.21∗∗∗0.10———(1.97)(2.28)(3.17)(2.36)ΔFt−8———0.28∗∗∗0.23∗∗∗—0.13∗∗∗———(3.72)(3.74)—(3.01)ΔFt−9————0.23∗∗∗—0.12∗∗————(3.89)—(2.89)R¯20.330.090.330.190.220.230.35F−Stat77.4314.1755.6314.5517.2629.9641.20LMχ232.0725.2929.0654.0751.1611.9151.25(0.13)(0.39)(0.41)(0.54)(0.11)(0.16)(0.11)Note. Figures in parenthesis refer to respective t-stat for the coefficients.∗∗∗,∗∗, and∗ represent statistical significance at 1%, 5%, and 10%, respectively. Statistical significance of coefficients is considered at 5% level of significance. F-statistics is significant at 1% level for all the commodities.LMχ2 value shows the chi-square value of Breusch–Godfrey LM test for serial autocorrelation.Table 10
Vector error correction model for futures price of the selected commodities.
CoefficientsSilverAluminumCopperLeadNickelZincCrude oilαF0.08∗∗∗0.10∗∗∗0.010.17∗∗0.050.07∗0.04∗∗(4.30)(4.50)(0.23)(3.19)(1.63)(2.04)(3.01)ΔSt−10.14∗∗∗0.20∗∗∗−0.020.22∗∗∗0.15∗∗∗0.12∗∗∗0.08∗∗(4.05)(7.34)(−0.03)(6.03)(3.90)(3.54)(3.16)ΔSt−20.08∗0.16∗∗∗0.010.18∗∗∗0.15∗∗0.10∗0.08∗∗(2.15)(5.32)(1.11)(4.29)(3.21)(2.48)(2.58)ΔSt−30.08∗0.13∗∗∗0.070.18∗∗∗0.17∗∗∗0.13∗∗0.08∗∗(1.97)(4.18)(0.23)(3.73)(3.42)(2.78)(2.75)ΔSt−40.060.13∗∗∗0.04∗0.15∗∗0.080.16∗∗∗0.11∗∗∗(1.54)(4.10)(1.02)(3.02)(1.62)(3.45)(3.66)ΔSt−50.10∗∗0.14∗∗∗0.030.17∗∗0.12∗0.17∗∗∗0.12∗∗∗(3.16)(4.17)(0.62)(3.22)(2.16)(3.54)(3.85)ΔSt−6——0.040.18∗∗0.080.12∗∗0.11∗∗∗——(0.05)(3.17)(1.56)(2.61)(3.40)ΔSt−7———0.15∗∗0.070.02−0.01———(2.66)(1.27)(0.52)(−0.258)ΔSt−8———0.21∗∗∗−0.09∗—0.05∗———(3.71)(−1.86)—(1.69)ΔSt−9————0.01—0.04————(0.04)—(1.63)ΔFt−1−0.07∗−0.14∗∗∗−0.02−0.08∗−0.04−0.050.02(−2.51)(−4.61)(−0.76)(−1.98)(−0.86)(−1.45)(0.65)ΔFt−2−0.10∗∗−0.15∗∗∗0.03−0.15∗∗−0.12∗−0.08∗−0.13∗∗∗(−2.77)(−4.43)(1.09)(−2.91)(−2.36)(−1.85)(−3.55)ΔFt−3−0.03−0.12∗∗∗0.02−0.21∗∗∗−0.23∗∗∗−0.15∗∗−0.09∗(−0.89)(−3.57)(0.81)(−3.73)(−4.11)(−2.86)(−2.33)ΔFt−4−0.09∗−0.11∗∗0.03−0.17∗∗−0.16∗∗−0.15∗∗−0.09∗(−2.25)(−3.01)(0.95)(−2.88)(−2.76)(−2.89)(−2.18)ΔFt−5−0.07∗−0.14∗∗∗0.07−0.22∗∗∗−0.060.20∗∗∗−0.13∗∗(−1.89)(−3.89)(2.32)(−3.50)(−0.96)(−3.53)(−3.26)ΔFt−6——0.03−0.22∗∗∗−0.09−0.19∗∗∗−0.12∗∗——(1.18)(−3.39)(−1.49)(−3.49)(−2.95)ΔFt−7———−0.20∗∗−0.09−0.09∗−0.09∗———(−3.04)(−1.47)(−1.85)(−2.34)ΔFt−8———−0.19∗∗0.01—−0.06———(−2.49)(0.03)—(−1.55)ΔFt−9————0.09—−0.04————(1.59)—(−1.08)R¯20.020.040.010.060.040.030.04F−Stat3.447.201.353.983.452.472.96LMχ232.0725.2929.0654.0751.1611.9151.25(0.13)(0.39)(0.41)(0.54)(0.11)(0.16)(0.11)


#### 5.5.1. Silver

The coefficient of the error correction termαs is negative and not significant. It implies that the spot price is not responding to the previous period’s equilibrium. αF is positive, which implies that silver’s futures price is responding positively to the previous period’s equilibrium. In ECM for spot price, the coefficients are negative and significant up to lag 5. However, the coefficients for the futures price are positive and significant up to lag 5. It shows that lagged spot price has a negative impact, and lagged futures price positively impacts the spot price. In ECM for the futures price, the spot price coefficients positively impact futures prices up to lag 5, whereas lagged futures price has a negative impact on the current futures price. Spot price at lag 1 has the highest impact on the current futures price than the higher lags. ECM result implies that the previous day spot prices have a positive impact on the futures price. Thus, it is established that the futures market leads the spot market and not vice versa in the price discovery process.


#### 5.5.2. Aluminium

The error correction term’s coefficient is negative and statistically not significant at 5% level of significance. In ECM for spot price, lagged spot price coefficients up to lag 5 are negative and statistically significant. It is found that the coefficients for both spot and futures prices are declining throughout the lag. It means that the previous spot price at lag 1 has a more negative impact on the current spot price than other previous prices at higher lags. Futures price coefficients are positively influencing the current spot price. In ECM for the futures price,αF is positive and statistically significant at 1% level. It shows that the futures price’s short-run deviations would be adjusted in an upward direction towards the long-run equilibrium. The coefficients for lagged spot prices positively impact the current futures price, and the coefficients of lagged futures prices have a negative impact on the current futures price. The results suggest that the futures market leads to the spot market, and the spot market does not lead to the futures market in price discovery.


#### 5.5.3. Copper

The coefficient of the error correction termαs is negative and statistically significant at 5% level. When αs is negative and statistically significant, spot price corrects the deviations from the long-run equilibrium. So, if the actual equilibrium value is high, the negative error correction term will reduce it, and if the equilibrium value is too low, the error correction term will raise it. The spot price is responsive to the previous period’s equilibrium error. In ECM for the spot price, the lagged spot price coefficients up to lag 5 are negative and statistically significant at 1% level, whereas lagged futures price coefficients are positive. ECM for the futures price (11) is not statistically significant. Therefore, the impact of the futures price in adjusting the error towards long-run equilibrium can be ruled out.


#### 5.5.4. Lead

The coefficient of the error correction termαs is negative and statistically not significant. In ECM for spot price, the spot price coefficients up to lag 6 are negative and statistically significant at 1% level. Previous spot price up to lag 8 has an impact on the current spot price, and the declining effect of the lagged spot price varies from −0.44 in lag 1 to -0.21 in lag 8. Futures price coefficients up to lag 8 affect the current spot price positively. In ECM for the futures price, αF is positive and statistically significant at 5% level. It shows that the futures price’s short-run deviations would be adjusted in an upward direction towards the long-run equilibrium. Coefficients for lagged spot prices up to lag 8 have a positive impact on the current futures price. Similarly, the coefficients for lagged futures prices up to lag 8 negatively affect the current futures price. The results also show that the futures market leads spot market in price discovery and not vice versa.


#### 5.5.5. Nickel

The coefficient of the error correction termαs s negative and statistically not significant. In ECM for spot price, the spot price coefficients up to lag 9 are negative and statistically significant at 1% level. Previous spot prices up to lag 9 impact the current spot price, and the declining effect of the lagged spot price varies from -0.48 in lag 1 to −0.15 in lag 9. Futures price coefficients up to lag 9 affect positively the current spot price. In ECM for the futures price, αF is positive and statistically not significant. So, it suggests that short-run deviations of the futures price are not adjusting towards the long-run equilibrium. The coefficients for lagged spot prices up to lag 3 have a positive impact on the current futures price. Similarly, the lagged futures price’s coefficients up to lag 6 have a negative impact on the current futures price. Thus, the results show that both the spot and futures markets are not adjusting in short-run deviations towards long-run equilibrium.


#### 5.5.6. Zinc

The coefficient of the error correction termαs is negative and statistically significant. When αs is negative and statistically significant, spot price corrects the deviations from the long-run equilibrium. The spot price is responsive to the previous period’s equilibrium error. In ECM for the spot price, coefficients up to lag 5 are negative and statistically significant. The result shows that coefficients for both spot and futures prices are declining for lag. It means that the spot price at lag 1 has a more negative impact on the current spot price than the spot price of higher lags. Futures price coefficients up to lag 6 are positively influencing the current spot price. In ECM for the futures price, αF is positive and statistically not significant. It implies that short-run deviations of the futures price are not adjusting towards the long-run equilibrium. The coefficients for lagged spot prices up to lag 6 positively impact the current futures price. Lagged futures price coefficients at lag 1 and lag 2 are statistically not significant. However, lagged futures price coefficients from lag 3 to lag 6 have a negative impact on the current futures price. Thus, it can be established that the spot market leads to the futures market and not vice versa.


#### 5.5.7. Crude Oil

The coefficient of the error correction termαs is negative and statistically significant. When αs is negative and statistically significant, the spot price corrects the deviations from the long-run equilibrium and responsive to the previous period’s equilibrium error. In ECM for the spot price, coefficients for lagged spot price up to lag 3 have a negative impact on the current spot price. Lagged futures prices up to lag 4, and at lag 8 and lag 9 are having a positive impact on the current spot price. Futures price coefficients are positively influencing the current spot price. In ECM for the futures price, αF is positive and statistically significant at 5% level. It shows that the futures price’s short-run deviations would be adjusted in an upward direction towards the long-run equilibrium. The coefficients for lagged spot price up to lag 5 have a positive impact on the current futures price, and the coefficients for lagged futures price at lag 1, lag 5, and lag 6 have a negative effect on the current futures price. Thus, both spot and futures markets contribute to the process of price discovery, as they can adjust to the short-run deviations towards the long-run equilibrium.VECM regressions for spot and futures prices are significant for silver, aluminum, lead, nickel, zinc, and crude oil. However, the error correction model for the futures price of copper is not statistically significant.R¯2 the error correction model for the spot price (10) is higher than the futures price (11). The results from the model’s estimation imply that the error correction term αs and the lagged futures and spot prices explain the model better than the futures price equation. Breusch–Godfrey LM χ2 test for serial autocorrelation is conducted to test the null hypothesis of no autocorrelation at the respective lag for all the commodities. Values are not statistically significant for all the commodities, which imply no autocorrelation problem in the dataset for all the commodities. It also confirms that the selected lags for the commodities are appropriate for estimating a vector autoregressive model.


## 5.1. Descriptive Statistics

Tables4 and 5 show the descriptive statistics of the selected commodities for spot and futures returns. The average percentage return in the spot market is higher than the futures market for all the commodities. However, the futures return is negative for zinc and natural gas, which implies a downward bias of futures prices in the futures market. The standard deviation is higher in the spot market for all the commodities than that in the futures markets. It also shows that the spot market is highly volatile than the futures market. The spot return’s unconditional distributions are negatively skewed for copper, whereas such distributions of the futures return are negatively skewed for gold, silver, aluminum, and zinc. Spot return distribution is platykurtic for gold, silver, lead, and zinc. However, the spot return distribution is leptokurtic for copper, nickel, crude oil, and natural gas. Spot return for aluminum shows the mesokurtic type of distribution. Futures return distribution is leptokurtic for all the commodities except zinc. Minimum spot return varies from −6.44% (for zinc) to −66.65% (for copper), and maximum spot return varies from 13.19% (for gold) to 82.70% (for natural gas), as shown in Table 4. Similarly, minimum futures return varies from −6.33% (for copper) to −15.90% (for silver), and maximum futures return varies from 5.47% (for gold) to 22.17% (for lead), as shown in Table 5.Table 4
Descriptive statistics of selected commodities for spot return.
GroupCommodityMeanStd. DevSkewnessKurtosisMinMaxJ-B statBullionGold0.01830.01990.2761−2.3658−0.06800.131944.4369Silver0.03380.02840.2558−2.5279−0.08350.161234.8346Base metalsAluminum0.02900.02470.39150.3661−0.08220.1703758.5985Copper0.01340.0526−3.240441.2291−0.66650.25381995.4000Lead0.01980.03320.1312−1.7161−0.10950.169277.1338Nickel0.02310.03920.57781.1388−0.11590.3037918.3396Zinc0.02880.03070.4878−1.6323−0.06440.1575168.4567EnergyCrude oil0.03370.04911.96765.8151−0.09520.42515898.1310Natural gas0.07900.11162.82577.6306−0.09120.82717752.7000Table 5
Descriptive statistics of selected commodities for futures return.
GroupCommodityMeanStd. DevSkewnessKurtosisMinMaxJ-B statBullionGold0.00070.0104−0.47983.3165−0.08000.05472550.9430Silver0.00100.0153−0.87398.4257−0.15910.08809547.0380Base metalsAluminum0.00020.0146−0.76206.9756−0.15610.05876458.7260Copper0.00050.01450.54252.0853−0.06330.10601652.9410Lead0.00030.02270.89766.7044−0.11440.22184343.0010Nickel0.00000.02260.27990.1735−0.10130.1315516.9168Zinc−0.00010.0195−0.0179−1.0128−0.08610.0832235.8748EnergyCrude oil0.00040.01670.05520.4974−0.08720.1078776.1763Natural gas−0.00020.02341.04164.5081−0.08920.19173249.1260


## 5.2. Stationarity Test

Augmented Dickey–Fuller (ADF) test results are presented in Table6. The test shows that the log of spot and futures prices for level is nonstationary for all the commodities, alike prior studies [15, 16, 18–20, 22, 23, 26, 28, 50]. The null hypothesis of nonstationary is statistically not significant for both the price series in the level. However, the null hypothesis is statistically significant at 1% level of significance for both the spot and futures prices in difference. Thus, the test indicates that the difference of log spot and futures prices is integrated with order 1 for all the commodities. The result of the unit root test directs to proceed for the cointegration analysis, where the first condition, i.e., both the series, must be nonstationary in level and integrated of order one for the Johansen–Juselius (J-J) test needs to be satisfied.Table 6
Unit root test of spot and futures prices (level and difference) for the selected commodities.
GroupLevels (log)First difference (log)CommodityConstraintSpotFutureConstraintSpotFutureIntegrationBullionGoldI and T−3.01−2.90I−10.48−10.42I (1)SilverI and T−1.72−2.12I−10.67−10.22I (1)Base metalsAluminumI and T−1.85−1.81I−10.37−10.77I (1)CopperI and T−1.90−2.15None−11.54−8.49I (1)LeadI−1.67−1.79None−9.74−9.71I (1)NickelI−1.89−1.73I and T−11.26−10.84I (1)ZincI−1.22−1.16None−10.69−10.50I (1)EnergyCrude oilI and T−1.76−1.80None−12.37−10.92I (1)Natural gasI−2.20−2.05None−10.12−10.27I (1)Note. The Fuller critical values for ADF test at 1%, 5%, and 10% are -3.43, −2.86, −2.57, respectively for constant. The Fuller critical values for ADF test at 1%, 5%, and 10% are -3.96, −3.41, and −3.12, respectively for constant + time trend (denoted by I and T). The Fuller critical values for ADF test at 1%, 5%, and 10% are −2.58, −1.95, and −1.62, respectively for no constant or time trend (denoted by none).


## 5.3. Granger Causality Test

Before estimating the cointegration test in vector autoregressive (VAR) framework, the Granger causality test is conducted to know if any unidirectional or bidirectional causality relationship exists between spot and futures prices, in line with earlier research [15, 18–20, 22]. Granger causality test is estimated following the equations (10) and (11). The estimation results from the Granger causality test are presented in Table 7. The null hypothesis that spot return does not Granger cause futures return is rejected for gold, silver, aluminum, lead, nickel, zinc, and crude oil. It implies that the spot returns cause futures returns in these commodities. The null hypothesis cannot be rejected for copper and natural gas. It implies that spot return does not cause futures return for copper and natural gas. The null hypothesis that futures return does not Granger cause spot return is rejected for all the commodities. Therefore, futures return Granger causes spot returns for all the commodities. Granger causality test suggests a bidirectional causality relationship between spot and futures prices for gold, silver, aluminum, lead, nickel, zinc, and crude oil. However, futures return does not Granger cause the spot return for copper and natural gas. As the Granger test suggests bidirectional causality between spot and futures prices for most of the commodities, there is a need to explore their meaningful relationship in the long run and short run using the J-J cointegration test followed by the estimation of a dynamic VECM.Table 7
Granger causality test of spot and futures returns for the selected commodities.
GroupCommoditySpot does not Granger cause futuresFutures does not Granger cause spotF-statP-valueF-statP-valueBullionGold6.0520.001175.1140.001Silver2.1930.031140.5480.001Base metalsAluminum9.2540.00123.9130.001Copper0.3910.89262.0220.001Lead5.2350.00137.2010.001Nickel3.1350.00146.2840.001Zinc3.1640.00169.6120.001EnergyCrude oil3.5420.001116.8420.001Natural gas0.7810.59276.0210.001Note. Spot and futures represent spot return and futures return, respectively. p value (0.001) refers to the significance at 1% level.


## 5.4. Johansen and Juselius (J-J) Cointegration Analysis

Following the stationarity test results of the previous section, the J-J cointegration test is estimated for the spot and futures prices, which are integrated of order one. Identification of the cointegrating relationship among the variables is important, as the VAR model in the first difference is misspecified for the two nonstationary variables, which are cointegrated. After identifying the cointegration relationship(4), VAR will include residuals from the vectors (lagged one period) in the VECM (Engle and Granger, 1987). The J-J cointegration test is estimated by following the Johansen and Juselius (1990) method. The results are presented in Table 8.Table 8
Johansen and Juselius cointegration rank test of spot and futures prices.
GroupCommodityLag lengthMaximum trace valueMaximum eigen valueRemarkH0: rank = 0 vs H1: rank = 1H0: rank = 1 vs H1: rank = 2H0: rank = 0 vs H1: rank = 1H0: rank = 1 vs H1: rank = 2BullionGold1018.842.4414.402.44NSSilver637.223.6533.573.651Base metalsAluminum660.952.8758.082.871Copper772.453.6668.803.661Lead955.103.3751.733.371Nickel1029.774.3125.464.311Zinc851.042.8548.192.851EnergyCrude oil1023.503.6520.853.651Natural gas414.903.0811.813.08NSNote. Critical values of λtracer=0 for 1%, 5%, and 10% significance levels are 24.6, 19.96, and 17.85, respectively. Critical values of λtracer=1 for 1%, 5%, and 10% are 12.97, 9.24, and 7.25, respectively. Critical values of λMaxr=0 for 1%, 5%, and 10% are 20.2, 15.67, and 13.75, respectively. Critical values of λMaxr=1 for 1%, 5%, and 10% are 12.97, 9.27, and 7.52, respectively. AIC lag selection criteria are used for the estimation.λtrace test rejects the null hypothesis of no cointegrating vectors r=0 at 1% significance level for silver, aluminum, copper, lead, nickel, and zinc, and it also rejects the same at 5% level for crude oil. Hence, it accepts the null hypothesis of more than zero cointegrating vectors. λtrace test accepts the null of no cointegrating vector in the case of gold and natural gas. It also accepts the r≤1 cointegrating vector’s null hypothesis against the alternative hypothesis of more than one cointegrating vectors r>1 for silver, aluminum, copper, lead, nickel, and zinc. Similarly, λmax test rejects the null hypothesis of no cointegrating vectors r=0 at 1% level of significance for silver, aluminum, copper, lead, nickel, zinc, and crude oil. So, it accepts the alternative hypothesis of one cointegrating vector r=1. λmax test accepts the null hypothesis of one cointegrating vector r=1 against the null hypothesis of two cointegrating vector r=2. Both λtrace and λmax tests suggest the presence of one cointegrating vector for silver, aluminum, copper, lead, nickel, zinc, and crude oil. The tests reject the presence of any cointegrating vector for gold and natural gas. Hence, a dynamic VECM is estimated for all those commodities, where there is a presence of a cointegrating relationship between the spot and futures prices.


## 5.5. Vector Error Correction Model

Results from the estimation of VECM (8) and (9) for spot and futures prices are presented in Tables 9 and 10. Accordingly, the results are interpreted for different commodities separately.Table 9
Vector error correction model for spot price of the selected commodities.
CoefficientsSilverAluminumCopperLeadNickelZincCrude oilαs−0.01−0.06∗−0.19∗∗−0.15∗−0.07∗−0.13∗∗∗−0.02∗∗∗(−0.98)(−2.44)(−8.34)(−2.54)(−2.17)(−3.45)(−1.39)ΔSt−1−0.43∗∗∗−0.25∗∗∗−0.25∗∗∗−0.44∗∗∗−0.48∗∗∗−0.57∗∗∗−0.43∗∗∗(−14.81)(−8.08)(−9.33)(−10.34)(−11.45)(−15.68)(−14.51)ΔSt−2−0.32∗∗∗−0.19∗∗∗−0.52∗∗∗−0.42∗∗∗−0.38∗∗∗−0.52∗∗∗−0.27∗∗∗(−10.20)(−5.65)(−19.63)(−8.38)(−7.76)(−11.10)(−8.31)ΔSt−3−0.23∗∗∗−0.17∗∗∗−0.24∗∗∗−0.35∗∗∗−0.28∗∗∗−0.40∗∗∗−0.17∗∗∗(−7.09)(−4.87)(−8.05)(−6.18)(−5.19)(−8.33)(−4.97)ΔSt−4−0.16∗∗∗−0.13∗∗∗−0.30∗∗∗−0.37∗∗∗−0.33∗∗∗−0.35∗∗∗−0.05(−5.09)(−3.61)(−10.93)(−6.15)(−6.02)(−6.90)(−1.39)ΔSt−5−0.06∗−0.11∗∗−0.23∗∗∗−0.32∗∗∗−0.25∗∗∗−0.26∗∗∗−0.04(−2.26)(−2.96)(−8.71)(−5.04)(−4.35)(−5.01)(−1.16)ΔSt−6——−0.23∗∗∗−0.23∗∗∗−0.20∗∗∗−0.21∗∗∗−0.04——(−8.97)(−3.47)(−3.43)(−4.12)(−1.06)ΔSt−7———−0.18−0.15−0.21−0.17———(−2.79)(−2.58)(−4.46)(−5.05)ΔSt−8———−0.21∗∗−0.29∗∗∗—−0.12∗∗∗———(−3.25)(−5.31)—(−3.49)ΔSt−9————−0.15∗∗—−0.14∗∗∗————(−3.08)—(−4.98)ΔFt−10.68∗∗∗0.39∗∗∗0.11∗∗∗0.73∗∗∗0.75∗∗∗0.78∗∗∗0.88∗∗∗(28.59)(11.65)(17.84)(14.64)(16.80)(20.19)(26.89)ΔFt−20.31∗∗∗0.22∗∗∗0.23∗∗∗0.51∗∗∗0.52∗∗∗0.66∗∗∗0.35∗∗∗(9.59)(5.86)(3.43)(8.54)(9.51)(13.57)(8.41)ΔFt−30.28∗∗∗0.11∗∗0.57∗∗∗0.39∗∗∗0.32∗∗∗0.49∗∗∗0.22∗∗∗(8.62)(2.95)(8.28)(5.99)(5.35)(8.97)(5.06)ΔFt−40.21∗∗∗0.17∗∗∗0.17∗0.37∗∗∗0.30∗∗∗0.39∗∗∗0.14∗∗∗(6.35)(4.44)(2.49)(5.28)(4.73)(6.75)(3.31)ΔFt−50.12∗∗∗0.09∗∗∗0.35∗0.33∗∗∗0.31∗∗∗0.28∗∗∗0.03(3.84)(2.21)(5.12)(4.47)(4.74)(4.69)(0.71)ΔFt−6——0.16∗0.21∗∗0.24∗∗∗0.22∗∗∗0.07——(2.31)(2.74)(3.66)(3.68)(1.64)ΔFt−7———0.15∗0.16∗0.21∗∗∗0.10———(1.97)(2.28)(3.17)(2.36)ΔFt−8———0.28∗∗∗0.23∗∗∗—0.13∗∗∗———(3.72)(3.74)—(3.01)ΔFt−9————0.23∗∗∗—0.12∗∗————(3.89)—(2.89)R¯20.330.090.330.190.220.230.35F−Stat77.4314.1755.6314.5517.2629.9641.20LMχ232.0725.2929.0654.0751.1611.9151.25(0.13)(0.39)(0.41)(0.54)(0.11)(0.16)(0.11)Note. Figures in parenthesis refer to respective t-stat for the coefficients.∗∗∗,∗∗, and∗ represent statistical significance at 1%, 5%, and 10%, respectively. Statistical significance of coefficients is considered at 5% level of significance. F-statistics is significant at 1% level for all the commodities.LMχ2 value shows the chi-square value of Breusch–Godfrey LM test for serial autocorrelation.Table 10
Vector error correction model for futures price of the selected commodities.
CoefficientsSilverAluminumCopperLeadNickelZincCrude oilαF0.08∗∗∗0.10∗∗∗0.010.17∗∗0.050.07∗0.04∗∗(4.30)(4.50)(0.23)(3.19)(1.63)(2.04)(3.01)ΔSt−10.14∗∗∗0.20∗∗∗−0.020.22∗∗∗0.15∗∗∗0.12∗∗∗0.08∗∗(4.05)(7.34)(−0.03)(6.03)(3.90)(3.54)(3.16)ΔSt−20.08∗0.16∗∗∗0.010.18∗∗∗0.15∗∗0.10∗0.08∗∗(2.15)(5.32)(1.11)(4.29)(3.21)(2.48)(2.58)ΔSt−30.08∗0.13∗∗∗0.070.18∗∗∗0.17∗∗∗0.13∗∗0.08∗∗(1.97)(4.18)(0.23)(3.73)(3.42)(2.78)(2.75)ΔSt−40.060.13∗∗∗0.04∗0.15∗∗0.080.16∗∗∗0.11∗∗∗(1.54)(4.10)(1.02)(3.02)(1.62)(3.45)(3.66)ΔSt−50.10∗∗0.14∗∗∗0.030.17∗∗0.12∗0.17∗∗∗0.12∗∗∗(3.16)(4.17)(0.62)(3.22)(2.16)(3.54)(3.85)ΔSt−6——0.040.18∗∗0.080.12∗∗0.11∗∗∗——(0.05)(3.17)(1.56)(2.61)(3.40)ΔSt−7———0.15∗∗0.070.02−0.01———(2.66)(1.27)(0.52)(−0.258)ΔSt−8———0.21∗∗∗−0.09∗—0.05∗———(3.71)(−1.86)—(1.69)ΔSt−9————0.01—0.04————(0.04)—(1.63)ΔFt−1−0.07∗−0.14∗∗∗−0.02−0.08∗−0.04−0.050.02(−2.51)(−4.61)(−0.76)(−1.98)(−0.86)(−1.45)(0.65)ΔFt−2−0.10∗∗−0.15∗∗∗0.03−0.15∗∗−0.12∗−0.08∗−0.13∗∗∗(−2.77)(−4.43)(1.09)(−2.91)(−2.36)(−1.85)(−3.55)ΔFt−3−0.03−0.12∗∗∗0.02−0.21∗∗∗−0.23∗∗∗−0.15∗∗−0.09∗(−0.89)(−3.57)(0.81)(−3.73)(−4.11)(−2.86)(−2.33)ΔFt−4−0.09∗−0.11∗∗0.03−0.17∗∗−0.16∗∗−0.15∗∗−0.09∗(−2.25)(−3.01)(0.95)(−2.88)(−2.76)(−2.89)(−2.18)ΔFt−5−0.07∗−0.14∗∗∗0.07−0.22∗∗∗−0.060.20∗∗∗−0.13∗∗(−1.89)(−3.89)(2.32)(−3.50)(−0.96)(−3.53)(−3.26)ΔFt−6——0.03−0.22∗∗∗−0.09−0.19∗∗∗−0.12∗∗——(1.18)(−3.39)(−1.49)(−3.49)(−2.95)ΔFt−7———−0.20∗∗−0.09−0.09∗−0.09∗———(−3.04)(−1.47)(−1.85)(−2.34)ΔFt−8———−0.19∗∗0.01—−0.06———(−2.49)(0.03)—(−1.55)ΔFt−9————0.09—−0.04————(1.59)—(−1.08)R¯20.020.040.010.060.040.030.04F−Stat3.447.201.353.983.452.472.96LMχ232.0725.2929.0654.0751.1611.9151.25(0.13)(0.39)(0.41)(0.54)(0.11)(0.16)(0.11)


### 5.5.1. Silver

The coefficient of the error correction termαs is negative and not significant. It implies that the spot price is not responding to the previous period’s equilibrium. αF is positive, which implies that silver’s futures price is responding positively to the previous period’s equilibrium. In ECM for spot price, the coefficients are negative and significant up to lag 5. However, the coefficients for the futures price are positive and significant up to lag 5. It shows that lagged spot price has a negative impact, and lagged futures price positively impacts the spot price. In ECM for the futures price, the spot price coefficients positively impact futures prices up to lag 5, whereas lagged futures price has a negative impact on the current futures price. Spot price at lag 1 has the highest impact on the current futures price than the higher lags. ECM result implies that the previous day spot prices have a positive impact on the futures price. Thus, it is established that the futures market leads the spot market and not vice versa in the price discovery process.


### 5.5.2. Aluminium

The error correction term’s coefficient is negative and statistically not significant at 5% level of significance. In ECM for spot price, lagged spot price coefficients up to lag 5 are negative and statistically significant. It is found that the coefficients for both spot and futures prices are declining throughout the lag. It means that the previous spot price at lag 1 has a more negative impact on the current spot price than other previous prices at higher lags. Futures price coefficients are positively influencing the current spot price. In ECM for the futures price,αF is positive and statistically significant at 1% level. It shows that the futures price’s short-run deviations would be adjusted in an upward direction towards the long-run equilibrium. The coefficients for lagged spot prices positively impact the current futures price, and the coefficients of lagged futures prices have a negative impact on the current futures price. The results suggest that the futures market leads to the spot market, and the spot market does not lead to the futures market in price discovery.


### 5.5.3. Copper

The coefficient of the error correction termαs is negative and statistically significant at 5% level. When αs is negative and statistically significant, spot price corrects the deviations from the long-run equilibrium. So, if the actual equilibrium value is high, the negative error correction term will reduce it, and if the equilibrium value is too low, the error correction term will raise it. The spot price is responsive to the previous period’s equilibrium error. In ECM for the spot price, the lagged spot price coefficients up to lag 5 are negative and statistically significant at 1% level, whereas lagged futures price coefficients are positive. ECM for the futures price (11) is not statistically significant. Therefore, the impact of the futures price in adjusting the error towards long-run equilibrium can be ruled out.


### 5.5.4. Lead

The coefficient of the error correction termαs is negative and statistically not significant. In ECM for spot price, the spot price coefficients up to lag 6 are negative and statistically significant at 1% level. Previous spot price up to lag 8 has an impact on the current spot price, and the declining effect of the lagged spot price varies from −0.44 in lag 1 to -0.21 in lag 8. Futures price coefficients up to lag 8 affect the current spot price positively. In ECM for the futures price, αF is positive and statistically significant at 5% level. It shows that the futures price’s short-run deviations would be adjusted in an upward direction towards the long-run equilibrium. Coefficients for lagged spot prices up to lag 8 have a positive impact on the current futures price. Similarly, the coefficients for lagged futures prices up to lag 8 negatively affect the current futures price. The results also show that the futures market leads spot market in price discovery and not vice versa.


### 5.5.5. Nickel

The coefficient of the error correction termαs s negative and statistically not significant. In ECM for spot price, the spot price coefficients up to lag 9 are negative and statistically significant at 1% level. Previous spot prices up to lag 9 impact the current spot price, and the declining effect of the lagged spot price varies from -0.48 in lag 1 to −0.15 in lag 9. Futures price coefficients up to lag 9 affect positively the current spot price. In ECM for the futures price, αF is positive and statistically not significant. So, it suggests that short-run deviations of the futures price are not adjusting towards the long-run equilibrium. The coefficients for lagged spot prices up to lag 3 have a positive impact on the current futures price. Similarly, the lagged futures price’s coefficients up to lag 6 have a negative impact on the current futures price. Thus, the results show that both the spot and futures markets are not adjusting in short-run deviations towards long-run equilibrium.


### 5.5.6. Zinc

The coefficient of the error correction termαs is negative and statistically significant. When αs is negative and statistically significant, spot price corrects the deviations from the long-run equilibrium. The spot price is responsive to the previous period’s equilibrium error. In ECM for the spot price, coefficients up to lag 5 are negative and statistically significant. The result shows that coefficients for both spot and futures prices are declining for lag. It means that the spot price at lag 1 has a more negative impact on the current spot price than the spot price of higher lags. Futures price coefficients up to lag 6 are positively influencing the current spot price. In ECM for the futures price, αF is positive and statistically not significant. It implies that short-run deviations of the futures price are not adjusting towards the long-run equilibrium. The coefficients for lagged spot prices up to lag 6 positively impact the current futures price. Lagged futures price coefficients at lag 1 and lag 2 are statistically not significant. However, lagged futures price coefficients from lag 3 to lag 6 have a negative impact on the current futures price. Thus, it can be established that the spot market leads to the futures market and not vice versa.


### 5.5.7. Crude Oil

The coefficient of the error correction termαs is negative and statistically significant. When αs is negative and statistically significant, the spot price corrects the deviations from the long-run equilibrium and responsive to the previous period’s equilibrium error. In ECM for the spot price, coefficients for lagged spot price up to lag 3 have a negative impact on the current spot price. Lagged futures prices up to lag 4, and at lag 8 and lag 9 are having a positive impact on the current spot price. Futures price coefficients are positively influencing the current spot price. In ECM for the futures price, αF is positive and statistically significant at 5% level. It shows that the futures price’s short-run deviations would be adjusted in an upward direction towards the long-run equilibrium. The coefficients for lagged spot price up to lag 5 have a positive impact on the current futures price, and the coefficients for lagged futures price at lag 1, lag 5, and lag 6 have a negative effect on the current futures price. Thus, both spot and futures markets contribute to the process of price discovery, as they can adjust to the short-run deviations towards the long-run equilibrium.VECM regressions for spot and futures prices are significant for silver, aluminum, lead, nickel, zinc, and crude oil. However, the error correction model for the futures price of copper is not statistically significant.R¯2 the error correction model for the spot price (10) is higher than the futures price (11). The results from the model’s estimation imply that the error correction term αs and the lagged futures and spot prices explain the model better than the futures price equation. Breusch–Godfrey LM χ2 test for serial autocorrelation is conducted to test the null hypothesis of no autocorrelation at the respective lag for all the commodities. Values are not statistically significant for all the commodities, which imply no autocorrelation problem in the dataset for all the commodities. It also confirms that the selected lags for the commodities are appropriate for estimating a vector autoregressive model.


## 5.5.1. Silver

The coefficient of the error correction termαs is negative and not significant. It implies that the spot price is not responding to the previous period’s equilibrium. αF is positive, which implies that silver’s futures price is responding positively to the previous period’s equilibrium. In ECM for spot price, the coefficients are negative and significant up to lag 5. However, the coefficients for the futures price are positive and significant up to lag 5. It shows that lagged spot price has a negative impact, and lagged futures price positively impacts the spot price. In ECM for the futures price, the spot price coefficients positively impact futures prices up to lag 5, whereas lagged futures price has a negative impact on the current futures price. Spot price at lag 1 has the highest impact on the current futures price than the higher lags. ECM result implies that the previous day spot prices have a positive impact on the futures price. Thus, it is established that the futures market leads the spot market and not vice versa in the price discovery process.


## 5.5.2. Aluminium

The error correction term’s coefficient is negative and statistically not significant at 5% level of significance. In ECM for spot price, lagged spot price coefficients up to lag 5 are negative and statistically significant. It is found that the coefficients for both spot and futures prices are declining throughout the lag. It means that the previous spot price at lag 1 has a more negative impact on the current spot price than other previous prices at higher lags. Futures price coefficients are positively influencing the current spot price. In ECM for the futures price,αF is positive and statistically significant at 1% level. It shows that the futures price’s short-run deviations would be adjusted in an upward direction towards the long-run equilibrium. The coefficients for lagged spot prices positively impact the current futures price, and the coefficients of lagged futures prices have a negative impact on the current futures price. The results suggest that the futures market leads to the spot market, and the spot market does not lead to the futures market in price discovery.


## 5.5.3. Copper

The coefficient of the error correction termαs is negative and statistically significant at 5% level. When αs is negative and statistically significant, spot price corrects the deviations from the long-run equilibrium. So, if the actual equilibrium value is high, the negative error correction term will reduce it, and if the equilibrium value is too low, the error correction term will raise it. The spot price is responsive to the previous period’s equilibrium error. In ECM for the spot price, the lagged spot price coefficients up to lag 5 are negative and statistically significant at 1% level, whereas lagged futures price coefficients are positive. ECM for the futures price (11) is not statistically significant. Therefore, the impact of the futures price in adjusting the error towards long-run equilibrium can be ruled out.


## 5.5.4. Lead

The coefficient of the error correction termαs is negative and statistically not significant. In ECM for spot price, the spot price coefficients up to lag 6 are negative and statistically significant at 1% level. Previous spot price up to lag 8 has an impact on the current spot price, and the declining effect of the lagged spot price varies from −0.44 in lag 1 to -0.21 in lag 8. Futures price coefficients up to lag 8 affect the current spot price positively. In ECM for the futures price, αF is positive and statistically significant at 5% level. It shows that the futures price’s short-run deviations would be adjusted in an upward direction towards the long-run equilibrium. Coefficients for lagged spot prices up to lag 8 have a positive impact on the current futures price. Similarly, the coefficients for lagged futures prices up to lag 8 negatively affect the current futures price. The results also show that the futures market leads spot market in price discovery and not vice versa.


## 5.5.5. Nickel

The coefficient of the error correction termαs s negative and statistically not significant. In ECM for spot price, the spot price coefficients up to lag 9 are negative and statistically significant at 1% level. Previous spot prices up to lag 9 impact the current spot price, and the declining effect of the lagged spot price varies from -0.48 in lag 1 to −0.15 in lag 9. Futures price coefficients up to lag 9 affect positively the current spot price. In ECM for the futures price, αF is positive and statistically not significant. So, it suggests that short-run deviations of the futures price are not adjusting towards the long-run equilibrium. The coefficients for lagged spot prices up to lag 3 have a positive impact on the current futures price. Similarly, the lagged futures price’s coefficients up to lag 6 have a negative impact on the current futures price. Thus, the results show that both the spot and futures markets are not adjusting in short-run deviations towards long-run equilibrium.


## 5.5.6. Zinc

The coefficient of the error correction termαs is negative and statistically significant. When αs is negative and statistically significant, spot price corrects the deviations from the long-run equilibrium. The spot price is responsive to the previous period’s equilibrium error. In ECM for the spot price, coefficients up to lag 5 are negative and statistically significant. The result shows that coefficients for both spot and futures prices are declining for lag. It means that the spot price at lag 1 has a more negative impact on the current spot price than the spot price of higher lags. Futures price coefficients up to lag 6 are positively influencing the current spot price. In ECM for the futures price, αF is positive and statistically not significant. It implies that short-run deviations of the futures price are not adjusting towards the long-run equilibrium. The coefficients for lagged spot prices up to lag 6 positively impact the current futures price. Lagged futures price coefficients at lag 1 and lag 2 are statistically not significant. However, lagged futures price coefficients from lag 3 to lag 6 have a negative impact on the current futures price. Thus, it can be established that the spot market leads to the futures market and not vice versa.


## 5.5.7. Crude Oil

The coefficient of the error correction termαs is negative and statistically significant. When αs is negative and statistically significant, the spot price corrects the deviations from the long-run equilibrium and responsive to the previous period’s equilibrium error. In ECM for the spot price, coefficients for lagged spot price up to lag 3 have a negative impact on the current spot price. Lagged futures prices up to lag 4, and at lag 8 and lag 9 are having a positive impact on the current spot price. Futures price coefficients are positively influencing the current spot price. In ECM for the futures price, αF is positive and statistically significant at 5% level. It shows that the futures price’s short-run deviations would be adjusted in an upward direction towards the long-run equilibrium. The coefficients for lagged spot price up to lag 5 have a positive impact on the current futures price, and the coefficients for lagged futures price at lag 1, lag 5, and lag 6 have a negative effect on the current futures price. Thus, both spot and futures markets contribute to the process of price discovery, as they can adjust to the short-run deviations towards the long-run equilibrium.VECM regressions for spot and futures prices are significant for silver, aluminum, lead, nickel, zinc, and crude oil. However, the error correction model for the futures price of copper is not statistically significant.R¯2 the error correction model for the spot price (10) is higher than the futures price (11). The results from the model’s estimation imply that the error correction term αs and the lagged futures and spot prices explain the model better than the futures price equation. Breusch–Godfrey LM χ2 test for serial autocorrelation is conducted to test the null hypothesis of no autocorrelation at the respective lag for all the commodities. Values are not statistically significant for all the commodities, which imply no autocorrelation problem in the dataset for all the commodities. It also confirms that the selected lags for the commodities are appropriate for estimating a vector autoregressive model.


## 6. Concluding Remarks and Policy Implications

The above empirical findings imply no lead-lag relationship between the spot and futures prices for gold, silver, aluminum, lead, nickel, zinc, crude oil, and natural gas. Market participants can use price as a source of information from both the spot and the futures markets. However, the spot markets do not impact the futures markets for copper and natural gas. The J-J cointegration test reveals that the spot and futures prices move together in a long-run equilibrium path for silver, aluminum, copper, lead, nickel, zinc, and crude oil. The test rejects any evidence of the cointegrating relationship of spot and futures prices for gold and natural gas. This implies the possibility of random walk nature in the spot and futures prices, and arbitrage fails to correct the disequilibrium.The existence of a cointegrating relationship implies that both the spot and futures markets may have short-run disequilibrium. However, this can be corrected by the arbitrage process. Spot markets play a crucial role in adjusting any short-run disequilibrium error for copper and zinc. However, futures market is more dominant in the case of silver, aluminum, and lead in adjusting the short-run disequilibrium. Both spot and futures markets are responsible for correcting the short-run disequilibrium for nickel and crude oil. As the Indian commodity futures market is growing rapidly, the findings have implications for the various market participants to implement trading and arbitrage strategy. It will also help the policy makers to check the stability of the market.Policymakers and regulators should highlight the efficiency of futures markets and enhance market participation by effectively applying trading strategies that allow market participants to take advantage of data accessibility [15]. In this regard, the outcomes can assist traders in more accurately estimating price changes, permitting them to confirm when investing and arbitraging opportunities emerge and how long they will persevere in the market [25]. As well, the Indian government should develop its institutional infrastructure to allow for more seamless commodity transactions consistent with market advances [23]. As such, expanded policies and enforcement are required, as well as expanded broker and dealer involvement in the commodities market, the insertion of exotic commodity derivatives, and heightened transparency and disclosure [17]. Besides, through investor awareness campaigns, the SEBI can strive to strengthen public awareness about the latest financial instruments [21].



---

*Source: 6431403-2022-03-08.xml*