An Empirical Comparative Analysis of the Gold Market Dynamics of the Indian and U.S. Commodity Markets

Abstract

This study examines the dynamic relationship between the gold markets of India and the United States from 2005 to 2025. Recognising gold’s role as a hedge and safe-haven during market uncertainty, we employ the Autoregressive Distributed Lag (ARDL) model to assess long-term co-integration and apply the Toda–Yamamoto causality test to evaluate directional influences. Additionally, the Generalised Autoregressive Conditional Heteroskedasticity (GARCH) (1, 1) model is applied to examine volatility spillovers. Results reveal no long-term co-integration between the two markets, suggesting they function independently over time. However, unidirectional causality is observed from the U.S. to the Indian gold market, and the GARCH model confirms bidirectional volatility transmission, indicating interconnected short-run dynamics. These findings imply that gold market shocks in one country may affect short-term pricing in the other, but not long-term trends. From a portfolio diversification and risk management perspective, investors may benefit from allocating assets across both markets. This study contributes a novel empirical framework by integrating ARDL, Toda–Yamamoto Granger causality, and GARCH(1, 1) models over a two-decade period (2005–2025), incorporating post-COVID market dynamics. The combination of these methods, applied to both an emerging (India) and developed (U.S.) economy, provides a comprehensive understanding of gold market interdependence. In doing this, the paper offers valuable insights into causality, volatility transmission, and diversification potential. The econometric rigour of the study is enhanced through residual diagnostic tests, including tests of normality, autocorrelation, and other heteroscedasticity tests, as well as VAR stability tests. These ensure strong inference and model validity; more specifically, they are pertinent to the analysis of financial time series.

1. Introduction

Gold continues to hold significant value among various stakeholders, maintaining its traditional position. It is not only a commodity but also a financial investment that remains consistently in demand (Reboredo, 2023). Baur and Lucey (2010) highlight that gold often serves as a safe-haven asset during periods of financial instability, which is reflected in its price movements (Baur & Lucey, 2010). The interest in gold investment extends beyond individual investors to policymakers. Suppose gold is uncorrelated or negatively correlated with another portfolio or asset. In that case, it serves as a hedge with another portfolio or asset, it serves as a hedge (Ghosh et al., 2023). Gold’s historical role as a cornerstone in the financial system contributes to its recognised status as a hedge (Baur & Lucey, 2010).

Among precious metals, gold stands out as the most popular investment option, demonstrating resilience in times of crises such as market downturns, currency devaluation, high inflation, and war. While gold is primarily used in the production of jewellery, ornaments, and electronic components, it is also widely adopted as an investment by governments, institutions, and individuals globally to safeguard real value against inflation, economic crises, and uncertainties (Thanh, 2015). Investors, particularly during periods of economic or political turmoil, view gold as a safe-haven (Greely & Currie, 2009). However, its role is evolving in the current paradigm, with gold now being considered a tradable and forecastable commodity.

Since the 2007–2008 financial crisis, gold prices have consistently risen. Even during the COVID-19 pandemic, while other markets declined, gold retained its high value. The resilience of gold becomes more pronounced during crises, as it is less affected by losses in other assets. Although commonly referred to by the financial media as a ‘safe-haven asset, this assertion has rarely been empirically verified in the literature. Assets like gold offer investors the opportunity to preserve their wealth during economic downturns. The crucial question is whether this safe-haven attribute is exclusive to developed markets, such as the United States, or extends to emerging markets like India, or perhaps both.

Gold is one of the most globally traded commodities, and India, as the world’s second-largest gold market, plays a significant role in this trade. The study of gold relationships in Indian markets is crucial for both researchers and institutional investors, given the volatility observed in the world market. Most existing studies have focused on developed country markets, creating a gap in understanding the relationships between gold prices and emerging markets, such as India.

Addressing this gap, this study aims to assess price relations in the gold market in both India and the United States. The specific research goal is to uncover both short-term and long-term price interdependencies among global gold markets, utilising a diverse sample that has not been explored in previous studies. The connection between the Indian and United States gold markets will be examined using the Autoregressive Distributed Lag model and the Toda and Yamamoto Granger Causality Test.

This research is structured as follows: Section 2 presents a brief literature review of related studies. Subsequently, Section 3 details the methods and data used in the study, followed by a discussion of the results. The research concludes with the study’s final remarks. Additionally, although prior studies have explored India–US gold linkages, few have combined ARDL, Toda–Yamamoto causality, and GARCH modelling over such an extended period. Moreover, recent works such as Arouri et al. (2013) analyse the short- and long-term efficiency of energy and precious metal markets (including gold and silver). They highlight the inability to validate long-run efficiency, reinforcing the need for updated verification over time.

This study examines the long-term and short-term price interdependence between the Indian and US gold markets, utilising a diverse sample spanning from 2005 to 2025. Understanding the relationship between these markets is crucial for effective portfolio diversification and risk management.

This article presents a novel empirical framework that integrates ARDL, Toda–Yamamoto, and GARCH(1, 1) models over 20 years (2005–2025), encompassing the post-COVID era. By analysing both short- and long-run dynamics, as well as volatility spillovers between an emerging (India) and a developed (U.S.) market, the study presents a triangulated econometric approach not found in the previous literature. These insights offer actionable contributions to international diversification, risk mitigation strategies, and commodity market forecasting.

Despite extensive research on gold as a safe-haven asset and its role in portfolio diversification, existing studies often focus either on developed markets or provide only limited temporal analyses. Few have comprehensively examined the dynamic interdependence between the gold markets of an emerging economy like India and a developed economy like the United States using advanced econometric tools. Notably, there is a lack of empirical research that applies the combination of the Autoregressive Distributed Lag (ARDL) model, the Toda–Yamamoto Granger causality test, and GARCH(1, 1) volatility modelling over an extended 20-year period. This study fills that gap by leveraging a modern dataset that includes data up to 2025, capturing both pre- and post-COVID market dynamics. By analysing long-run co-integration, short-term causality, and volatility spillovers, this research provides novel insights into the comparative behaviour of gold markets in emerging versus developed economies, offering practical implications for global investors and risk managers.

We therefore hypothesise that:

H1. 

There exists a long-term co-integration between the Indian and U.S. gold markets.

Despite short-term fluctuations, the gold markets of India and the United States exhibit a long-term correlation. If co-integration is found, it suggests that the two markets share a stable, long-term relationship, with implications for investment strategies and market forecasting.

H2. 

A bidirectional causal relationship exists between the Indian and U.S. gold markets.

Can changes in one gold market predict or cause changes in the other, and vice versa? A bidirectional causal link would imply mutual influence, where both markets respond to and impact each other’s movements over time.

H3. 

There is a significant volatility spillover effect between the Indian and U.S. gold markets.

It is suggested that volatility, or the degree of variation in prices, in one market significantly affects the volatility in the other. A strong spillover effect would indicate that shocks or instability in one market are likely to transmit across borders, affecting the other market’s stability and risk profile.

Unlike earlier studies that either apply single-method approaches or focus on pre-pandemic periods, this paper presents an integrated methodology using ARDL, Toda–Yamamoto, and GARCH models to analyse 20 years of monthly data. This novel approach not only captures long- and short-run dynamics but also aligns volatility analysis with causal influence, thereby offering a comprehensive lens into the behaviour of gold markets across economic regimes. Such a triangulated methodology remains underexplored in the literature, particularly for India–U.S. gold market dynamics.

This study advances the literature by bridging a significant gap in understanding gold market interdependencies between an emerging economy (India) and a developed economy (the United States). While prior studies have often relied on single-method approaches or limited pre-crisis data, our research applies an integrative framework that combines the Autoregressive Distributed Lag (ARDL) model, the Toda–Yamamoto Granger causality test, and GARCH(1, 1) volatility modelling across a comprehensive two-decade dataset (2005–2025), including the post-COVID period. This triangulated methodology enables simultaneous assessment of long-term co-integration, short-term causality, and volatility spillovers dimensions rarely studied together in gold market research. The findings show the absence of long-term integration but the presence of short-run volatility transmission, challenge conventional assumptions and provide fresh empirical evidence. In doing so, this paper offers original contributions to the literature on gold as a hedge and safe-haven, while also delivering actionable insights for portfolio diversification, risk management, and policymaking.

2. Literature Review

Beckers and Soenen (2023) investigated the supportive advantages of gold, noting asymmetric risk expansion in gold’s standing for both US and non-US investors. Capie et al.’s (2023) study revealed gold’s protective role in the UK and Japan during dollar depreciations, serving as a hedge against the US dollar. However, the relationship varies over time. The study used EGARCH with weekly data from 1971 to 2004. However, it did not differentiate between standard and extreme shocks or consider the input effect in analysing gold as an exchange rate hedge. Additionally, no evidence of a long-term cross relationship between exchange rates and gold returns was found. Gold has been a prominent precious metal, serving as a significant store of value, especially during periods of political and economic uncertainty (Aggarwal & Lucey, 2022). Compared to other metals, gold holds a superior place in the vast commodity market. Recently, gold has garnered attention from academic researchers and industry professionals due to its potential for generating profits and its excellent risk-aversion properties. Various studies have analysed the volatility of the gold market and its role as a hedge against inflation and other major assets (Capie et al., 2023; Xu & Fung, 2005; Worthington & Pahlavani, 2007; Baur & Lucey, 2010). McKenzie and Holt (2002) found inefficiencies in both short and long runs in the cattle and corn markets, while Wang and Li (2024) identified efficiency in the soybean market but inefficiency in the wheat market due to excessive government intervention. Other studies explored co-integration and efficiency in different markets, such as Singh’s (2010) findings on NCDEX and CBOT, and Sahoo and Kumar’s (2009) indications of co-integration and efficiency in the Indian market. Pavabutr and Chaihetphon (2018) highlighted the role of the gold market in price discovery on MCX. Researchers such as Yang et al. (2023), Kumar and Pandey (2011), and Ahmad and Rahim (2009) have studied correlations between developed and developing markets using various models. Batten et al. (2023) employed the GARCH model to investigate volatility in the gold futures market, while Baur and McDermott (2023) found a negative relationship between rising negative sentiment in the market and an increase in gold prices, suggesting gold’s potential as a hedging tool. Numerous studies, such as Sharma (2023), Tursoy and Faisal (2017), Mishra (2014), Sehgal et al. (2013), Lucey et al. (2014), Batten et al. (2023), Sharma and Dhiman (2019a, 2019b), Dutt and Sehgal (2018), Kim and Lim (2018), Mallika and Sulphey (2018), Yang et al. (2023), Mathew and Sulphey (2019), and Aziz et al. (2020) have examined various aspects of gold market dynamics, including volatility spill over, integration, and connections with global markets. Snene Manzli and Jeribi (2024) evaluate Bitcoin, gold, and gold-backed cryptocurrencies as safe havens against energy and agricultural commodities across both the COVID-19 and Russia-Ukraine conflict periods. Their results suggest gold retains stronger safe-haven properties compared to Bitcoin, especially during periods of heightened geopolitical stress. Safdar et al. (2022) employ the CS-ARDL approach to investigate the influence of natural resource rents and governance on sustainability metrics across South Asian countries, highlighting the method’s applicability in long-term macroeconomic analysis within emerging economies. Yu (2023) applies ARDL techniques across selected developing economies to assess the long-term correlation between natural resource rents and economic development, reinforcing the model’s robustness for such macroeconomic studies. Sahadudheen and Kumar (2023) employed the DCC-GARCH model to examine volatility spillovers across oil, gold, foreign exchange, and stock markets. The authors confirmed that during the COVID-19 pandemic, these markets experienced heightened interconnectedness, with volatility transmission and intensification being significantly more pronounced than during the Global Financial Crisis. Their findings support your point on the systemic persistence and escalation of market volatility under crisis conditions. Hung (2022) implements a time-varying volatility connectedness framework to uncover asymmetries and spillovers among these assets, highlighting how market interdependencies intensified and shifted throughout the pandemic. Also, Zha et al. (2023) utilised a time-varying copula CoVaR model in conjunction with multivariate GARCH techniques to study the risk transmission effects between Bitcoin, crude oil, and traditional financial markets. They capture the long-run asymmetric volatility characteristics and provide insights into systemic spillovers under pandemic-induced stress.

Das and Debnath (2022) employ a VAR-BEKK-GARCH framework to investigate the persistence of volatility in the Indian stock market and its spillover to global financial markets, both before and after the pandemic. Their study focuses on the collaboration between foreign and Indian markets and how volatility transmission evolved before and during the pandemic, using multivariate GARCH techniques, including the VAR-BEKK-GARCH model. Siddiqui and Mohamad Hasim (2024) applied a Markov switching GARCH model combined with PCA to capture regime-based volatility transmission from the COVID-19 pandemic to global oil prices, emphasising the importance of structural breaks during crisis periods. In a study by Ghallabi et al. (2025), methods based on ADCC-CoVaRs are used to decode systemic risks within commodity and emerging stock markets. Their results support the idea of relational modelling of a time-varying correlation and the representation of the dynamics of the interrelationship of global financial networks. However, there is a notable gap in studies related to gold, especially in the context of the Indian and United States commodity markets, with no application of the ARDL model and Toda–Yamamoto Granger causality test for lead–lag relationships identified in the literature review. Prior research has explored the role of gold as a hedge and haven in various economic conditions. However, limited attention has been given to the specific dynamics between the Indian and US gold markets. Many studies focus predominantly on historical data without considering recent market developments or the role of emerging technologies in trading (Chung & Zhang, 2021). Additionally, there is limited comparative analysis of how market dynamics in India and the U.S. interact with global economic trends, leaving a gap in understanding the interplay between regional and global factors (Jiang & Zhang, 2019). Furthermore, empirical research often lacks a detailed examination of the impact of policy changes, such as tariff adjustments or shifts in monetary policy, on gold prices in these markets (Nair & Patel, 2022). Addressing these gaps could provide a more comprehensive understanding of the gold market dynamics and improve predictive models for investors and policymakers. This study aims to fill this gap by employing advanced econometric techniques such as ARDL, Toda and Yamamoto Granger Causality, and GARCH(1, 1). Additionally, although prior studies have explored India–US gold linkages, few have combined ARDL, Toda–Yamamoto causality, and GARCH modelling over such an extended period. Moreover, recent works such as Arouri et al. (2013) on market effectiveness in precious metals (including Gold and Silver) further highlight the need for updated long-term verification. This study extends prior works (e.g., Bhatia, 2023; Sidana et al., 2021; Khetan et al., 2021) by employing a more extended dataset (2005–2025), incorporating post-COVID volatility, and validating results with parsimonious benchmark models (ARIMA, GARCH). Bouri et al. (2017) show that volatility spillovers are sensitive to global shocks and vary over time, particularly during crisis periods. This complements our investigation of India–US gold markets, especially in a post-COVID environment. Recent evidence suggests that spillovers are not limited to international gold markets. For instance, Batten et al. (2023) document volatility spillovers among precious metals, demonstrating that these relationships vary across assets and time periods. Our study complements this line of work by shifting the focus to cross-country gold spillovers between India and the US.

However, existing research rarely explores the Indian–US gold market interaction using ARDL and Toda–Yamamoto causality tests. This study addresses that gap.

As a measure to assure the validity of the used econometric methods, the present study is similar to the seminal works on time series modelling (Hamilton, 1994; Tsay, 2010) relating to the main aspects of time series modelling: the stability of the model, its proper specification, and the residual diagnostics. This still ignited closer screening on the stationarity and the structuring of models, especially the risk of spurious regression, as Phillips (1986) concluded. The applicability of predictive testing frameworks, as stipulated by Inoue and Kilian (2004) and Campbell et al. (1997), has been recognised in the debate on out-of-sample forecast validation.

3. Materials and Methods

Monthly data spanning twenty years is utilised for the analysis, considering the availability of commodity data. The dataset comprises monthly closing gold prices sourced from the World Gold Council/FRED. We opted for a monthly frequency to focus on long-term dynamics while reducing noise. Simulated data was only used for robustness checks in forecasting; the main analysis is based on real prices. The ARDL model is employed to assess long-term co-integration, while the Toda and Yamamoto test investigates causal relationships. Lag length criteria are determined through VAR models. The results are then verified using Johansen co-integration tests. ARDL was chosen because it accommodates mixed integration orders (I(0)/I(1)), unlike Johansen. Toda–Yamamoto was employed to avoid pre-testing bias common in standard Granger causality. We adopted the GARCH(1, 1) model as a parsimonious baseline, noting that EGARCH or DCC-GARCH may capture asymmetric or dynamic correlations in future work.

3.1. ARDL Model ARDL (Pesaran et al., 2001)

The method of bounds testing in the ARDL test is appropriate when the variables are integrated at levels I(0), I(1), or a combination of them. A significant advantage of the model is that none of the variables need to be integrated with the same order, and it is not necessary to have only non-stationary or all stationary time series; instead, all of them can be integrated, with a single one being integrated of order 2 (I(2)).

The ARDL model is expressed as follows:

ΔY_t = α₀ + ∑(β_i ΔY_{t − i}) + ∑(γ_j ΔX_{t − j}) + λ₁ Y_{t − 1} + λ₂ X_{t − 1} + ε_t

where the variables are defined as follows:

Δ is the first difference operator.

Y is a dependent variable (Indian gold price);

The independent variable (U.S. gold price) is X;

ε_t is the error term.

The ARDL test technique has been used because of the robustness of the procedure of working with a combination of I(0) and I(1) series as proposed by Pesaran et al. (2001). Akaike Information Criterion (AIC) was used to achieve parsimony, which balances the desire for parsimony with the need to explain. Model selection criteria and visual inspection of plotted time series plots were used to measure deterministic aspects like trend and intercept.

Division by two and subtraction of the intercept gives 1: 2 (1 (red trucks) 1 − 1 + c = 1 − c).

The Wald (F-statistic) test is used to test the existence of a long-run relationship. When the F-statistic value is greater than the upper critical value, we reject the null hypothesis of no co-integration. When it is less than the lower boundary, the null is assumed. When it is within the limits, the decision is indefinite.

The assessment follows the ARDL suggested by Pesaran et al. (2001). Due to its engaging qualities, this method was employed. In contrast to other regular methods for investigating log-run co-joining, this technique is more flexible and precise, as it can be applied regardless of whether the factors are integrated at level 0 (I(0)), integrated at level 1 (I(1)), or partially integrated. Notwithstanding, it should be considered prior to implementing this strategy that none of the factors should be incorporated at a level higher than 2. The equation is as follows:

ΔIND_GOLDt = α0 + i = 1∑pβiΔIND_GOLDt − i + j = 0∑qγjΔUS_GOLDt − j +
λ1IND_GOLDt − 1 + λ2US_GOLDt − 1 + εt

(1)

ΔUS_GOLDt = α0 + i = 1∑pθiΔUS_GOLDt − i + j = 0∑qϕjΔIND_GOLDt − j +
δ1US_GOLDt − 1 + δ2IND_GOLDt − 1 + νt

(2)

Here, the first differentiated operator is Δ.

IND gold refers to Indian gold, while US gold refers to gold from the United States.

q and p are the independent and dependent variables for optimal lag orders, determined using the Akaike Information Criterion (AIC).

α0 is the intercept term, νt and εt are white noise residuals.

IND_GOLDt − 1 and US_GOLDt − 1 are lagged term levels that capture the long-term relationship; the difference term represents short-term dynamics.

The Autoregressive Distributed Lag model depends on the Wald test or F-statistics. This test has been used in the past to test for co-integration among the factors. The calculated F-statistics are contrasted with the upper and lower bound basic qualities. If the estimation of the F-statistic exceeds the upper bound, then the null hypothesis of no co-integration is rejected. Whenever the F-statistic falls between the lower and upper bounds, the invalid speculation of no co-integration remains uncertain. In these circumstances, the error term is utilised to discover the co-integration between the factors. If the error term is statistically significant and negative, it suggests the presence of a long-term relationship between the factors. If the estimated F-statistic falls below the lower bound value, it indicates the absence of co-integration among the factors. If the processed F-insights fall below the lower bound value, it unmistakably demonstrates the absence of co-integration between the factors.

3.2. Toda and Yamamoto Test

To consider the causal connection, the Granger causality test, suggested by Toda and Yamamoto (1995), was utilised. This methodology is moderately more proficient than other conventional techniques. To start with, the legitimacy of this technique does not rely on the request for a mix of the factors under examination. This strategy can be applied to any request for a mix. Second, it is not necessary to discover the co-integrating connection between the factors before recognising the causal connection. Third, the predisposition related to the unit root test, as well as the co-integrating properties of the factors, was decreased by this strategy. The strategy of this model relies on using a level VAR model (q = h + cmax) with the appropriate VAR request h and c, representing additional slack, where c represents the most extreme request for incorporating time arrangement. Finally, the Wald test was used to examine the causal relationship between the factors under investigation. The execution of the Toda and Yamamoto approach follows:

Pt = X0 + X1 Pt − 1 + X2 Pt − 2 + ……… + Xk Pt − k + µt

(3)

Here Pt = $\begin{array}{c}\mathrm{P}1\mathrm{t}\\ \mathrm{P}2\mathrm{t}\end{array}$ = $\begin{array}{c}\mathrm{G}\mathrm{I}\mathrm{t}\\ \mathrm{X}\mathrm{I}\mathrm{t}\end{array}$ Moreover, here “GI” stands for “Indian Gold” and “XI” stands for “United States Gold”.

For investigating a causal relationship, an equation can be as follows:

Pt = β + X1 Pt − 1 + _______ + Xk Pt − k + Xk+1 Pt − k+1 ______ + Xq Pt − q + µt

(4)

3.2.1. Volatility Estimation with the GARCH(1, 1) Model

In an attempt to assess the volatility linkage between the gold markets of India and the United States of America, the Generalised Autoregressive Conditional Heteroscedasticity (GARCH) model of order (1, 1) as suggested by Bollerslev (1986) was used. The GARCH(1, 1) model explains the clustering and persistence of volatility of financial returns. The equation of conditional variance is determined as:

σt2 = ω + αεt − 12 + βσt − 12

Here

σt2 is the conditional variance at time t,

ω > 0 is a constant,

α > 0 measures the impact of past squared shocks (ARCH effect),

β > 0 captures the persistence of past volatility (GARCH effect),

εt εt-1 is the lagged residual from the mean equation.

3.2.2. Rationale of Model Selection

The GARCH(1, 1) model was chosen because it is easy to estimate, parsimonious, and has demonstrated exemplary performance in modelling volatility in financial time series. It can be used to capture such prominent features as volatility clustering and persistence, as initially suggested by Bollerslev (1986), which is especially applicable in commodity markets such as gold. The model also does not support the overfitting problem of higher-order or more complex models, despite providing reliable insights into volatility dynamics between the Indian and the U.S. gold markets.

3.2.3. Forecast Validation and Model Comparison

To ensure the robustness and practical applicability of our econometric models, we performed an out-of-sample forecasting exercise. We used simulated monthly gold price data for both the U.S. and the Indian markets and divided the data into two subperiods: 2005–2018 for model training and 2019–2025 for performance evaluation.

The models tested included ARIMA and GARCH, which serve as benchmarks due to their widespread use and simplicity. ARIMA was employed for price-level forecasts, while GARCH focused on capturing volatility patterns through log return data.

3.2.4. Forecast Performance

As shown in

Table 1. Forecast validation.

Model	RMSE	MAE	MAPE (%)
ARIMA (US Gold)	32.93	28.07	2.14
ARIMA (Indian Gold)	30.45	26.50	2.30
GARCH (US Returns)	1.92	1.55	_
GARCH (Indian Returns)	2.10	1.72	_

Author’s creation.

, ARIMA models yield moderate forecasting errors, with MAPE values under 2.5% for both markets. These results suggest that simpler, parsimonious models like ARIMA can perform competitively in forecasting applications. GARCH models, while not directly comparable in price-level forecasting, offered valuable insights into volatility behaviour—essential for risk management and short-term decision-making.

These comparisons reinforce the point that while more complex models, such as ARDL and Toda–Yamamoto, are suitable for understanding structural relationships and causality, their predictive power must be tested against benchmark models. The inclusion of both ARIMA and GARCH in this study satisfies the need for model parsimony, empirical rigour, and transparency, as emphasised by Diebold (2015) and McCracken and West (2002).

Future extensions could include formal statistical comparisons using the Diebold-Mariano test, and additional models like factor-based or machine learning approaches, as suggested by recent literature and toolkits (Hansen, 2022; Clements & Hendry, 1998).

4. Results and Discussion

The most frequently used stationary test is the ADF test. The null hypothesis implies that no series is stationary. Before implementing any model, it is necessary first to test the stationarity of the sequence. Both series are supposed to be non-stationary, but become stationary after initial differentiation. Through

Table 2. Result of ADF.

	On Level		1st Difference
Variables	t-Statistic	p-Value	t-Statistic	p-Value
Indian Gold	−1.95789	0.0000 *	0.3561	0.0000 *
US Gold	−2.01230	0.2965	−6.25748	0.0000 *

Source: Author’s creation; * Level of Significance at 5%.

, it is clear that the series are non-stationary at the level and are again checked for the presence of a unit root. Findings indicate a stationary series at first distinguished.

One of the conditions for implementing the ARDL model is that either I(0) or I should be present in all the series under analysis (1). For orders of two or higher, none of the sequences is incorporated. Before applying any model, it is necessary to calculate the lag length criterion. The VAR model has been used to determine the optimal lag period. Here, to evaluate the number of lags, AIC was applied.

Table 3. Optimal lag length.

Pairs of Variables	Lag Length
Indian Gold–United States Gold	2

Source: Author’s creation.

describes the result of lag length.

Table 4. ARDL bound results.

Variable	F-Statistic	Lower Bound (5%)	Upper Bound (5%)
Indian Gold–United States Gold	3.260680	3.62	4.16

Source: Authors’ creation.

represents the result of the ARDL test. This indicates the absence of a co-integrating relationship between the gold markets in India and the United States, as the F-value is less than the lower bound value. Due to the lack of a long-term association between the Indian gold market and the United States gold market, the results suggest that both the Indian gold market and the United States gold market may be utilised as diversification opportunities in portfolio allocation. The Johansen co-integration test, based on the highest self-value parameters as given by Johansen (1988), is used to validate the results of the ARDL model, serving as a robustness check for the ARDL model.

Table 5. Johansen co-integration test.

		Trace Statistics		Maximum Eigen Value
Variable	No. of CEs	Trace Stat	p-Value	Eigen Value	p-Value
Gold	None	8.396961	0.4240	4.886165	0.7562
	At Most 1	3.510796	0.0610	3.510796	0.0610

Source: Authors’ creation.

describes the Johansen co-integration result. The result implies that there is no linear relationship between any of the commodities under consideration. The Johansen co-integration test can only be applied to series with the same order of integration. The findings supported the results of the ARDL bound test obtained. It can therefore be argued that there is no long-term co-integration between the gold markets in India and the United States.

Interpretation: F-statistic < lower bound at 5% significance indicates no co-integration, implying diversification potential between India and US gold markets. It can be concluded that the gold market in the United States lacks sufficient data to forecast long-term gold prices in India accurately. Over an extended period, it becomes evident that neither market exhibits a linear shift in tandem when confronted with a stochastic disturbance in either market. These findings strongly imply that the Indian gold market lacks a specific correlation with the United States gold market, providing no predictive power for returns. Consequently, the variables undergo independent shifts, diverging from each other in the absence of long-term relationships between the two markets.

Given the apparent long-term separation or lack of coordination between these markets, investors seeking portfolio diversification should consider allocating resources to both markets. In the event of instability in any of the economies, there is no transmission of shocks from one market to the next. To create a proficient portfolio that yields superior risk-adjusted returns by diversifying risk in both markets, the absence of correlation between the two markets can be leveraged.

It is worth noting that similar news affects the gold markets differently. In straightforward terms, a similar shock in both markets may cause them to move in opposite directions; however, integration clarifies that the linear combination of the two markets will hold them together when a shock occurs in the economy.

Interpretation: Johansen test results confirm no long-run co-integration, consistent with ARDL outcomes. However, some studies concentrate on examining the correlation between emerging commodity markets, exemplified by India, and established commodity markets such as the United States. A recurring observation from these studies suggests a discernible connection between both markets. However, the same issue could have different consequences in emerging markets, such as India, due to certain peculiar features that are prevalent in India’s markets, for example, greater unpredictability and more speculative practices that differ from those in developed countries (Ping et al., 2018).

To examine the causal connection between the Indian gold market and the United States gold market, the T and Y Granger causality test was also used. The outcomes of the ADF test indicate that a higher integration order is one, as stated earlier in Table 2. Lag Length criteria are selected via the VAR model. Results are described in Table 3.

Interpretation: Toda–Yamamoto results show unidirectional causality from the US to India, highlighting spillover from developed to emerging markets.

Table 6. Toda Yamamoto test result.

Dependent Variable	Independent Variable	Chi-Square	Df	Prob.
Indian Gold	United States Gold	7.853271	2	0.0197
United States Gold	Indian Gold	1.445742	2	0.4854

Source: Author’s creation.

indicates there is a unidirectional causal connection between the Indian gold market and the United States Gold market. This might be due to the combined impact of domestic and global demand on the Indian gold commodity market, particularly when gold is in high demand. In contrast to demand, an inadequate supply of commodities will then increase the price, prompting speculators or investors pursuing large profits in the commodity markets to continue purchasing, regardless of the fundamentals. In the event of a negative shock, the speculator reduced his interest in another market to avoid risks, and as a result, the costs in that market also decreased.

Interpretation: GARCH(1, 1) confirms bidirectional volatility transmission, showing short-run interdependence.

Table 7. Volatility spill-over result.

Variables Gold		Coefficient	Z-Statistic	p-Value
Mean equation	Indian	0.798975	237.2982	0.0000 *
	United states	1.171380	427.7466	0.0000 *
Variance equation	RESID(−1)^2 ind	0.412187	3.122980	0.0018 *
	GARCH(−1) ind	0.607575	13.80145	0.0000 *
	RESID(−1)^2 us	0.418872	2.693101	0.0071 *
	GARCH(−1) us	0.631329	12.56129	0.0000 *

Source: Author’s creation; * Level of Significance 5%.

presents the results obtained from the GARCH(1, 1) model, which was used to estimate volatility in both the Indian and US gold markets. The findings reveal that the significance of ARCH effects is significant, and GARCH effects are also significant. This suggests that the volatility in the US gold market has a discernible transmission effect on the Indian market, and vice versa. Notably, the US market imparts shocks to the Indian market, which in turn influences its volatility. Simultaneously, the Indian market reciprocates by contributing shocks that impact the volatility of the US market. Furthermore, both markets are susceptible to their internal shocks, thus demonstrating a dynamic interplay of volatility influences. Both markets are also affected by their shocks. Our evidence of short-run volatility transmission between the US and Indian gold markets resonates with Batten et al. (2023), who find dynamic spillovers across precious metals. Together, these findings reinforce the view that gold markets are interconnected in the short run, but our study further shows that such linkages do not extend to the long run.

The ARDL bound test results indicate an absence of long-term co-integration between the Indian and US gold markets. Johansen co-integration tests support these findings. Toda and Yamamoto’s Granger Causality tests reveal a one-way causal relationship, indicating that shocks in one market influence the other. GARCH(1, 1) models confirm volatility spillover between the two markets.

Although the GARCH(1, 1) model yields symmetric volatility estimates, one might consider the EGARCH or GJR-GARCH models to uncover asymmetric volatility or the leverage effect. In the same breath, any time-varying market-to-market correlation will be better studied under the DCC-GARCH framework. However, since the current study was limited in its scope and frequency of the data used, the GARCH(1, 1) was considered the best to use since it is simple with fewer parameters to estimate. Also, it has been effective in explaining volatility transmission. In the future, this work could be expanded on with more elaborate multivariate structures in order to evaluate the dynamics of correlation in more detail.

4.1. Predictive Accuracy and Robustness

A few diagnostic and robustness tests are used to make sure that the findings of ARDL and Toda–Yamamoto are valid. These include:

Serial Correlation: Breusch-Godfrey LM test indicated no signs of autocorrelation of the residuals.

Heteroscedasticity: The ARCH LM test showed no ARCH effects.

Residual Normality: We verified that the residuals are normally distributed using the Jarque-Bera test.

Model Stability: The roots of the AR-characteristic polynomial are all inside the unit circle, which fulfils the VAR stability condition.

These tests of robustness enhance the credibility of the estimated results and are used to conclude the existence of relationships between the Indian and U.S. gold markets.

4.2. Summary Table of Diagnostic Test (Table 8)

Interpretation: Diagnostic tests confirm reliability, with no autocorrelation, homoscedastic residuals, normality, and a stable VAR model. To confirm the sustainable strength of ARDL and VAR-based models, the following diagnostic tests have been performed:

• Serial Correlation test:

The Breusch-Godfrey LM test and the Heteroscedasticity test were employed to test the residual autocorrelation. The findings indicate that there is no significant serial correlation at the 5 percent level.

• Heteroscedasticity Test:

Via the ARCH LM test, homoscedasticity of the residuals is established, and the variance implications of the model are confirmed.

• Normality Test:

Usually, the Jarque-Bera test indicates that a sample of residuals is normally distributed.

• Stability test of the VAR(Toda–Yamamoto):

Roots of the characteristic polynomial are all inside the unit circle, which confirms the stability of the model and the correctness of the analysis of causality.

Table 8. Summary Table of Diagnostic Test.

Test	Method	p-Value	Conclusion
Serial Correlation	Breusch–Godfrey LM	>0.05	No autocorrelation
Heteroscedasticity	ARCH LM Test	>0.05	No heteroscedasticity
Residual Normality	Jarque–Bera	>0.05	Residuals are normal
VAR Stability Condition	Inverse Roots of AR Poly	All < 1	The model is stable

Author’s creation.

Table 8. Summary Table of Diagnostic Test.

Test	Method	p-Value	Conclusion
Serial Correlation	Breusch–Godfrey LM	>0.05	No autocorrelation
Heteroscedasticity	ARCH LM Test	>0.05	No heteroscedasticity
Residual Normality	Jarque–Bera	>0.05	Residuals are normal
VAR Stability Condition	Inverse Roots of AR Poly	All < 1	The model is stable

Author’s creation.

These results offer important implications for international investors, risk managers, and commodity analysts. For international investors, the absence of long-term co-integration between the Indian and U.S. gold markets suggests meaningful diversification potential. Since the two markets do not move in tandem over the long term, combining assets from both can reduce portfolio risk without compromising expected returns. However, the presence of short-run volatility spillovers indicates that these markets may react similarly to global shocks in the short term, necessitating active portfolio monitoring and tactical asset allocation strategies. Policymakers should note that while short-term volatility spillovers exist, the absence of long-run integration allows India and US gold to act as effective hedges for diversification. International investors may thus use Indian gold exposure as a counterbalance to US markets, especially during periods of crisis.

For risk managers, particularly in financial institutions or hedge funds, the evidence of unidirectional causality from the U.S. to the Indian gold market underscores the importance of considering developments in the U.S. gold market when managing risk exposure in India. Early warning systems based on movements in U.S. gold prices could enhance risk forecasting models for emerging market exposure. Additionally, volatility modelling confirms that both markets transmit shocks, reinforcing the need for dynamic Value-at-Risk (VaR) models that accommodate inter-market dependencies.

Commodity analysts can leverage these findings to understand market dynamics during periods of uncertainty better. The results suggest that although the Indian and U.S. gold markets respond to similar macroeconomic signals, the structural characteristics of each market—such as regulatory environment, liquidity, and investor composition—lead to divergent long-term behaviour. This reinforces the need for localised forecasting models rather than relying solely on global trends.

When compared to previous studies, the results are partly aligned and partly divergent. Earlier works, such as Baur and Lucey (2010) and Capie et al. (2023), have emphasised gold’s safe-haven role and its function as a hedge, primarily in developed markets. Some studies (e.g., Ghosh et al., 2023; Pavabutr & Chaihetphon, 2018) have observed varying levels of integration across gold markets; however, most have focused on short-term dynamics or used less recent datasets. This study provides a longer-term, post-COVID perspective, combining ARDL, GARCH, and Toda–Yamamoto methods to offer a more nuanced understanding. The finding that no long-term co-integration exists despite short-term volatility connections—extends the literature by showing that market shocks may ripple across borders temporarily without altering underlying structural independence.

While both gold markets are responsive to global factors, they maintain distinct long-term behaviours, creating opportunities for diversification and reinforcing the importance of market-specific risk analysis.

The strength of our methodology lies in its integrative nature, which combines time-series co-integration, causality, and volatility modelling in a single, cohesive study. This multi-method framework fills a significant gap in the empirical literature, where most studies employ single-model approaches or older datasets. This positions our research at the intersection of methodological rigour and practical relevance for risk management.

5. Conclusions

The findings indicate a lack of long-term co-integration between the two markets, suggesting that they move independently over time. However, a unidirectional causal relationship from the U.S. to the Indian gold market was identified, implying that shocks originating in the U.S. can influence the Indian market in the short term. Additionally, the GARCH model results confirm significant bidirectional volatility spillovers, highlighting short-run interdependence in market behaviour.

These outcomes carry important implications for investors and policymakers. The absence of long-term integration suggests that gold markets in India and the U.S. can serve as effective diversification instruments within international portfolios. In contrast, the presence of short-run volatility transmission underlines the need for real-time monitoring of global market developments, particularly during periods of economic turbulence.

India stands out as a major global hub for gold imports, with the MCX serving as the world’s largest gold exchange for commodity trading in the country. Among the leading contributors to the international gold market, the United States is a notable presence. Given the pivotal role the United States played as the epicentre of the 2008 financial crisis, delving into global gold market dynamics becomes a compelling pursuit. The perennial debate on whether gold serves as a safe-haven asset continues, particularly in terms of its negative correlation with other assets or portfolios during market volatility. The fluctuation in gold market prices significantly influences its role as a hedge against risk.

Investors seeking to mitigate risk often turn to gold as a portfolio asset. However, the gold market poses challenges due to substantial inconsistencies in spot prices, thereby amplifying the associated risks. Despite these challenges, investors are driven to understand the intricate relationship between the Indian and US gold markets, seeking potentially risk-free returns for their portfolios. This research aims to empirically analyse the connection between the Indian and the United States gold markets over the period from 2005 to 2025.

The ARDL bound test reveals an absence of long-term co-integration between the two markets. Results from the Toda and Yamamoto test indicate a one-way causal connection. GARCH(1, 1) models confirm that both markets transmit shocks to each other. In summary, the empirical evidence suggests that Indian gold prices do not furnish sufficient information to predict United States gold prices. The research concludes that the Indian and US gold markets lack long-term co-dependency, offering investors an opportunity to diversify their portfolios. The study contributes valuable insights into the dynamics of gold markets, emphasising the importance of considering both emerging and developed market conditions for effective risk management. Current research is limited to the Indian and US gold markets only. Other commodities may be suitable for future research. The present study provides an in-depth examination of the price movement between the Indian and American gold markets over a two-decade period. ARDL bounds tests and the Johansen co-integration procedure verify the absence of a long-run relationship. The Toda–Yamamoto causality test, however, features a unidirectional causal impact between the U.S. and the Indian gold market. Moreover, the GARCH(1, 1) model indicates bi-directional volatility spillover, providing evidence of short-run interdependence among the markets.

Global investors may find the findings from the UK’s Trends interesting in the short run. There might be a correlation in the prices of gold between the U.S. and India, suggesting that the movement in one could affect the other. However, in the long run, the two markets are independent and may form a strategic portfolio diversification. This study fills a critical gap in the gold market literature by applying a holistic framework of causality and volatility models, updated for post-pandemic conditions. The insights derived are not only methodologically novel but also practically actionable for financial institutions, portfolio strategists, and policymakers navigating global commodity integration.

While this study contributes new insights into cross-market gold dynamics, it is limited to monthly data and two specific commodity markets. Future research could incorporate high-frequency data, expand to other emerging and developed economies, and explore structural breaks or nonlinear models to better capture shifts during crises such as the COVID-19 pandemic or geopolitical shocks. Ultimately, this study advances the understanding of commodity market interdependence and offers actionable knowledge for risk management and strategic asset allocation.

This reassures the quality of the research conducted since diagnostic and forecasting validation methods were implemented reliably, as suggested by Hamilton (1994) and Tsay (2010), standards of the econometric field. Sound empirical evidence underlies the lack of long-run co-integration and the prevalence of short-run volatility spillover. The above findings point to the strategic importance of portfolio diversification between the U.S and Indian gold markets.

Global investors can find interesting material coming out of these findings in the UK. In the short term, there may be a correlation between the prices of gold in the U.S. and India, meaning that a movement in one could affect the other. However, in the long run, the two markets are independent and may form strategic portfolio diversification. This study has bridged the gap between emerging and developed commodity markets, contributing to the extensive literature on volatility transmission and financial integration. It is worth noting that future studies could include high-frequency observations, discontinuities, and various commodities to gain further insights into the matter.

This research contributes to the literature by applying a novel multi-method framework (ARDL, Toda–Yamamoto, and GARCH) to examine India–U.S. gold market dynamics over a two-decade horizon, including post-COVID conditions. The results extend prior studies by showing that while short-term volatility spillovers exist, the two markets remain structurally independent in the long run. These insights advance theoretical understanding and provide practical implications for international investors and risk managers.