Research on Efficiency and Multifractality of Gold Market under Major Events

Abstract

(1) Background: As a safe-haven asset, gold attracts a large number of investors during major events. Uncertainties caused by global economic and market conditions lead to increased purchases of gold by investors, which in turn affects the efficiency of the gold market. (2) Methods: This article focuses on Shanghai gold and explores the potential impacts of different major events on the effectiveness and risk of China’s gold market using the Multifractal Detrended Fluctuation Analysis (MFDFA) method. (3) Results: the Chinese gold spot market is anti-persistence and exhibits significant multifractal characteristics, suggesting that the gold spot market possesses predictability and has significant volatility and high risk. Furthermore, the study conducts stage analysis based on different major events, and the results are as follows. The empirical results show that the gold market exhibits anti-persistence and multifractality features for three major events, i.e., the US–China trade war, the COVID-19 pandemic, and the Russia–Ukraine War. (4) Conclusions: for the COVID-19 pandemic, the intensity of anti-persistence is the highest. In addition, it is also found that the stronger the anti-persistence in the gold markets under a given event, the greater the corresponding risk. Finally, the article provides relevant decision-making suggestions for investors and risk managers.

1. Introduction

Throughout human civilization, gold has been the most important precious metal, circulated as a legal standard currency for a long time. With the progress of society, the credit-based currency system gradually replaced physical currency, leading to the decline of the precious metal currency era. But gold still occupied a very important position due to its scarcity and high industrial value. During periods of geopolitical tension and economic turmoil, people often turn to gold as a wealth store. Since the 20th century, gold has been widely utilized in the financial domain because of its unique attributes as a currency, commodity, and safe-haven asset. The gold market is a global financial market with various trading forms, including spot market, future market, gold derivatives market, gold ETF, and gold fund. Investors can allocate assets through gold exchange-traded funds (ETFs) or gold funds, which can directly or indirectly affect the price of gold.

Since the 21st century, various types of major events have occurred frequently. With the deepening of globalization, a crisis in one country will also have different degrees of impact on the economic development of other countries. The subprime mortgage crisis in 2008 led to a global economic crisis. In addition, the outbreak of the 2015 Chinese stock market crash triggered a decline in the US stock market. Subsequently, the 2018 US–China trade war had a significantly negative impact on the import-export trade of both countries. Besides, the infectious pneumonia epidemic caused by the novel coronavirus COVID-19, with its unprecedented infectivity and destructive power, has brought extremely serious consequences to all aspects of human society. The global economy suffered greatly, and the financial market has not been immune. Circuit breakers have occurred in the international stock market many times, and the price of oil spots has even fallen into negative territory. In 2022, the Russia–Ukraine war caused serious economic consequences for Europe and the world. In this context, precious metals, as traditional safe-haven assets, have garnered much attention for their price trends. Among these assets, gold has become an important choice for investors due to its unique commodity attributes, monetary status, and financial value. It is highly favored by those seeking safe-haven investments. China is currently in a critical period of economic recovery and new development after experiencing the impact of many major events. Under the current economic conditions, investors’ tendencies to avoid risks are becoming increasingly significant, and this sentiment is diffused in the market. How to stabilize the financial market amid exogenous shocks and exploring the “safe harbor” of asset allocation has become an urgent issue for market participants and scholars. In view of the special status of the gold market during major events, studying its market efficiency and price fluctuation patterns before and after these events is of significant theoretical support and practical significance. Deeply understanding the dynamic response mechanism of the gold market under major shocks can effectively prevent potential market risks and promote the efficiency of the market. It not only enriches the theoretical framework of the gold market but also provides a basis for policymakers to make decisions.

The remainder of this article is organized as follows: Section 2 presents a literature review. Section 3 provides the data collection and methodology explanation. The empirical results are provided in Section 4. Finally, Section 5 provides the conclusions.

2. Literature Review

From the development history of the Efficient Market Hypothesis (EMH), the concept was initially proposed by Gibson (1889) [1]. Fama et al. (1970) proposed a widely recognized definition of the efficient market and improved the division of these three forms [2]. Based on information related to asset pricing, Robert proposed three types of classification distinguishing efficient markets: If market prices have fully reflected all historical information, it is considered weak-form market efficiency. If market prices incorporate past price information and other publicly available information, it is considered a semi-strong-form efficient market. If prices include not only information exclusive to that market but also all publicly available information, it is considered a strong-form efficient market [3].

On the basis of the efficient market theory, many scholars have studied the gold and gold spot markets. Weston (1987) tested the weak inefficiency of the gold market in New York [4]. In the assumptions of EMH, a linear paradigm is used to characterize the market. However, financial markets typically exhibit nonlinearity and complexity. In 1975, Mandelbrot proposed the concept of fractals, suggesting that fractal characteristics exist in both natural and social systems. In 1994, Peter applied the Hurst index and fractal Brownian motion to capital markets, introducing the Fractal Market Hypothesis (FMH) [5]. Mills (2004) used the DFA method to analyze the statistical characteristics of daily gold price data in the London gold market from 1971 to 2002. By detrending the time series of gold prices with irregular local trends, he analyzed the volatility of gold returns. And in the long run, the Gauss feature is restored [6]. With the continuous improvement of China’s economic system, the emergence of the Shanghai gold market has prompted many domestic scholars to conduct research on the gold market. Yang and Wu (2013) analyzed the data from international gold, silver, platinum, and palladium spot markets from 2000 to 2012 and found that the market did not meet the standard of a weakly efficient market, with incomplete information or insufficient response. The study also shows that the volatility of these markets has a leverage effect, especially in the case of gold, whose price fluctuations have a significant impact on other commodities [7]. Fan (2019) used the random walk test, the EG two-step cointegration test, and the Hurst index analysis based on R/S analysis to explore the effectiveness of the gold future market. The conclusion showed that there was a significant cointegration relationship between the gold spot market and the gold future market, and the gold future market did not exhibit weak effectiveness [8]. Based on the concept of market effectiveness, Yang and Liu (2023) selected the price data samples of domestic and foreign gold spot markets and future markets from January 2010 to December 2020 for empirical testing and found that the spot and future prices of China’s gold market were interdependent in a long-term equilibrium and affected each other in a certain period of time. The price discovery function of the gold future to the spot market was relatively effective [9]. Using the seasonal and trend decomposition and MFDFA method, Bhatia investigated the efficiency of the gold returns for India, the USA, and Brazil. The results showed that India and the USA presented persistence in small fluctuations, while Brazil displayed persistent behavior in large fluctuations during the COVID-19 pandemic and post-COVID-19 pandemic periods [10].

Many factors affect the price of gold spot. Not only supply and demand profoundly impact the gold spot market, but a confluence of diverse factors, such as the dynamics of substitute markets and the overall macroeconomic environment, also jointly shape the intricate landscape of the gold market. Valadkhan et al. (2022) deeply discussed the interaction and potential connections among the US dollar index, nominal effective exchange rate index, and gold price [11]. Wang et al. (2021) found that the intensification of geopolitical risks will promote the price of gold market, and investors prefer to buy gold as a hedge asset in a high-risk environment [12]. After in-depth research, Wang (2022) pointed out that although major geopolitical risk events, such as wars, had a certain impact on the gold price, this impact is mainly concentrated in the short term and does not always lead to a rise in the gold price [13]. Yao (2021) used the HAR and its extended model to analyze the price fluctuation of the gold market in the Shanghai Spot Exchange after the launch of night trading. The results showed that the realized volatility of China’s gold market possessed a significant easing trend [14]. Mensi et al. (2021) analyzed the dynamic asymmetric return spillover effect of gold and oil commodities on 22 European stock sectors. The results stated that gold and oil markets tended to be the main recipients of spillover [15]. Taking the gold markets of Shanghai and London as case studies, Zhu (2022) explored the dynamic adjustment of domestic and foreign gold market prices in the process of seeking market equilibrium during the COVID-19 pandemic and found that the two markets showed obvious co-movement [16]. By constructing a modified DCC-MIDAS model and introducing the Economic Policy Uncertainty Index (EPU) as the research variable, Yang et al. (2021) found that when the economic policy uncertainty was high, investors preferred to choose gold as a relatively safe investment asset [17]. Alexandros and Kyriakopoulos analyzed the volatility transmission between the gold and silver markets from a long-term perspective [18]. Zheng et al. (2021) explored the dynamics of the gold market using VECM, impulse response analysis, and variance decomposition. They found a stable equilibrium between international gold spot prices and factors like geopolitical risks, economic policy uncertainty, the US dollar index, interest rates, inflation, and global gold supply–demand gaps. Among them, the US inflation level and the US dollar index had a particularly significant impact on the international gold spot price [19].

Following these studies above, significant contributions have been made to explore the hedging capabilities of gold spot and future markets. Li et al. (2021) examined the hedging capabilities of gold spots from perspectives of volatility forecasting and price co-movement, confirming its role as a “hedge haven” for other assets during unstable times like geopolitical conflicts, wars, and financial crises [20]. Based on the geopolitical risk factors, Liang et al. (2022) used the GARCH-MIDAS model to explore the volatility of China’s gold spot contract and found that geopolitical tensions or unstable events would trigger the volatility of the gold market, thus affecting the price [21]. Based on the GED-GARCH (1,1) model, Chiang (2022) analyzed the returns of gold in five regions, including the United States, the United Kingdom, the European Union, China, and India. The empirical results showed that gold can effectively hedge the uncertainty [22]. Selmi et al. (2022) used the Markov switching copula model to analyze the role of gold in fierce geopolitical conflicts and found that gold could act as a safe asset [23].

Yuan and Feng (2024) deeply analyzed the hedging ability of different gold assets to the Chinese stock market and the stock market of various industries and proved that under the impact of major crisis events, the hedging ability of domestic gold to the Chinese stock market is stronger than that of international gold, and the hedging ability of spot gold to the Chinese stock market is stronger than that of gold spot [24]. Tan and Tian (2021) used the dynamic conditional correlation mixed-frequency data sampling model to test the hedging effect of gold spots. The results showed that the hedging effect of the international gold spot on the US stock market was not obvious, but it had a significant hedging effect [25].

Based on the multifractal detrended volatility analysis (MF-DFA) method, Wang et al. (2011) investigated the multifractal characteristics of gold spot prices in the New York Commodity Exchange and found that the gold market always showed higher efficiency [26]. Sun and Wang (2015) conducted an in-depth analysis of the multifractal characteristics of gold and silver spot markets by applying the extended bipartite overlapping smooth window MF-DFA method. The results illustrated that, compared to the gold market, the silver market had a higher risk, while the gold market demonstrated a stronger hedging ability, highlighting its robustness as a hedge asset [27]. Oral and Unal (2019) explored the linkage dependence and multifractal characteristics among three precious metals, namely gold, silver, and platinum [28]. Liu and Wang (2022) used the multifractal analysis method to study the multifractal characteristics and interaction correlation of the Shanghai gold spot market, the London gold spot market, and China’s foreign exchange market. They found that there were multifractal characteristics in all three markets [29]. Guo et al. (2021) utilized the multifractal asymmetric detrended interactive correlation analysis (MF-ADCCA) method and found that the interactive correlation between gold price and trading volume had significantly different fluctuation characteristics under different trends, indicating that the relationship between the two is not simply linearity [30].

On the whole, there is much research on gold spot and future markets domestically and internationally. However, most studies have relied primarily on linear models for empirical analysis. Considering the complex nonlinear characteristics of the gold market, based on the MFDFA method, this paper will further comprehensively analyze the effectiveness and complexity of China’s gold spot market in combination with the specific background of major events. The empirical results show that the gold market exhibits anti-persistence both overall and under three major events, indicating market predictability. Especially for the COVID-19 pandemic, the intensity of anti-persistence is the highest. Besides, it is also found that the stronger the anti-persistence in the gold markets under a given event, the greater the corresponding risk.

3. Data and Methods

In the empirical part, the daily closing price of Shanghai’s gold spot from 26 January 2011 to 31 July 2024 is selected to represent the market price of gold in China. Utilizing the MFDFA method and the event analysis method, this study delves into the effectiveness and complexity of gold spot, considering the overarching and staged perspectives. Data are from https://wind.com.cn and accessed on 31 July 2024, and all works are implemented on the MATLAB2018a and Eviews11 platforms.

This paper studies the effectiveness and complexity of the gold spot market under the background of different events and the multifractal characteristics through the MFDFA method, including the following six steps:

Step 1: Calculate the return rate: $\left\{r_t\right\}$

$$r_t=\mathit{log}{P}_t-\mathit{log}{P}_{t-1},t=\mathrm{1,2},\dots N.$$

(1)

Construct a new sequence: $\left\{y_t\right\}(1\le t\le N)$

$$y_t=\sum _{i=1}^{t}r\left(i\right),t=\mathrm{1,2},\dots N.$$

(2)

First, a time series $r_t$ of length N is assumed, and the time series is divided into N/S intervals of length S, whose intervals do not overlap each other. In order to ensure that all data are processed to prevent tail data loss, the time series is again divided into intervals of length S from back to front.

Step 2: Perform a least squares fitting on $\left\{y_t\right\}(1\le t\le N)$ to obtain first-order or second-order polynomials, i.e., the fitted values ${\widehat{y}}_{t,v}$, and calculate the residuals:

$${\epsilon }_t=\left(y_t-{\widehat{y}}_{t,v}\right)$$

(3)

Assume that $y_t$ exhibits some trend features. To remove the influence of this trend and extract the true signal, the detrended fluctuation analysis method employing a polynomial fitting is used to eliminate the upward or downward trend. In N/S regions, the trend is eliminated by least squares fitting polynomial to obtain the corresponding residual sequence. Furthermore, we calculate the average residual square:

$${\epsilon }_t={{(y}_t-{\widehat{y}}_{t,v})}^2$$

(4)

Step 3: Repeat Step 2, summing the squared residuals for each interval in N/S regions. Use least squares polynomial fitting to remove trends, obtaining the corresponding residual sequence, where v denotes the v-th interval, and S represents the length of each subinterval. Calculate the subinterval variance function of the v-th sub-intervals:

$$F^2\left(s,v\right)={\displaystyle \frac{1}{s}}\sum _{t=1}^s{\left(y_{t,v}-{\widehat{y}}_{t,v}\right)}^2$$

(5)

Given the order q, the q-order fluctuation function is calculated and denoted by $F_q\left(s\right)$. Due to the sequence length N not always being a multiple of S, it results in residual data at the end. To ensure all data are processed without losing the trailing data, the time series is divided into intervals of length s from the end backward. This yields $2\left[N/S\right]$ intervals, denoted as $N_s$ = $\left[N/s\right]$, from which the v-order fluctuation function $F_q\left(s\right)$ of the sequence can be calculated as follows:

$$F^2\left(s,v\right)={\displaystyle \frac{1}{s}}\sum _{t=1}^s{\left(y_{t,v}-{\widehat{y}}_{t,v}\right)}^2$$

(6)

$$F_q(s)=\{\begin{array}{c}{\left({\displaystyle \frac{1}{2N_s}}{\displaystyle \sum _{v=1}^{2N_s}}{\left[F^2\right(s,v\left)\right]}^{{\displaystyle \frac{q}{2}}}\right)}^{{\displaystyle \frac{1}{q}}},q\ne 0\\ \mathit{exp}({\displaystyle \frac{1}{4N_s}}{\displaystyle \sum _{v=1}^{2N_s}}ln[F^2(s,v)\left]\right),q=0\end{array}$$

(7)

where $q=2$ is used to study market efficiency:

$$F_2\left(s\right)={({\displaystyle \frac{1}{2N_s}}\sum _{v=1}^{2N_s}\left[F^2\left(s,v\right)\right])}^{{\displaystyle \frac{1}{2}}}$$

(8)

Step 4: Change the value of $S$, $S=5,6,7,8,\dots N/4,$ by analyzing $S$ and the logarithmic graph of $F_q\left(s\right)$ with respect to different values of A, it is determined that $F_q\left(s\right)$= A$S^{h\left(q\right)}$ forms a power law relationship:

$$\mathit{log}{F}_q\left(s\right)=logA+h\left(q\right)\mathit{log}s$$

(9)

The estimated value of the generalized exponent is obtained by the least square method. When $q=2$, $H\left(2\right)$ denotes the Hurst index. If the market is efficient, $H\left(2\right)=0.5$, the market is weak-efficient. If $H\left(2\right)>0.5$, the market has positive persistence, i.e., if it rose before, it will continue to rise after, and vice versa. When $H\left(2\right)<0.5,$ the market has the characteristics of anti-persistence; that is, the price has fallen before, and then there will be an upward trend, and vice versa.

$H\left(q\right)$ is also often used to judge the risk degree of the market. When $H\left(q\right)$ fluctuates significantly, it implies that the price fluctuations of the time series are large, indicating higher market risk. The index of $H\left(q\right)$ can also study the size of the market fluctuation range when q is a small negative, $H\left(q\right)$ reflecting the small fluctuation dominated the scaling behavior. When $H\left(q\right)$ > 0.5, it indicates that small fluctuations exhibit positive persistence in the market, meaning that an upward trend in the earlier period is likely to continue in the later period and vice versa. When $H\left(q\right)$< 0.5, it indicates negative persistence. When q is a large positive number, $H\left(q\right)$ measures the dominance of large fluctuations. When $H\left(q\right)$ > 0.5, it indicates positive persistence, and when $H\left(q\right)$ < 0.5, it indicates negative persistence.

Step 5: Determine the time series multifractality by analyzing the multifractal spectrogram based on the generalized exponent $H\left(q\right)$ and scaling exponent $\tau \left(q\right)$ obtained from the MFDFA method.

$$\tau \left(q\right)qh\left(q\right)-1$$

(10)

In addition, the quality index $\tau \left(q\right)$ can also represent the multifractal characteristics of the time series, i.e., $\tau \left(q\right)$ reflects the complexity of $q$ the market. When the function is nonlinear, the series has multifractal characteristics. The mono-fractal market is relatively simple, and the market risk is small. It is relatively simple to make a portfolio for the mono-fractal market, while the multifractal market is more complex, and the corresponding risk is greater. Therefore, the multifractal portfolio is more complex than the mono-fractal when considering the risk and return.

Then, through Legendre transformation, the singular index $\alpha$, which is used to describe the singular degree of the time series, and the multifractal spectrum $f\left(\alpha \right)$ reflecting the fractal dimension are obtained:

$$\alpha ={\displaystyle \frac{d}{d\left(q\right)}}\tau \left(q\right)=h\left(q\right)+q{h}^{\prime }\left(q\right)$$

(11)

$$f\left(\alpha \right)=q\left[\alpha -h\left(q\right)\right]+1$$

(12)

The multifractal strength can be defined from Equations (13) and (14):

$$∆\alpha ={\alpha }_{max}-{\alpha }_{min}$$

(13)

$$∆f=f\left({\alpha }_{min}\right)-f\left({\alpha }_{max}\right)$$

(14)

The $∆\alpha$ measures the extent of fluctuations in returns, both in upward and downward trends. When ∆α approaches 0, it indicates that the market has low volatility and is mono-fractal. The larger the ∆α, the greater the market’s volatility and risk. It is indicated that the market is multifractal. When $∆\alpha =0$, it means that the time distribution of the return series is completely uniform. $∆f$ reflects the frequency of changes in high and low prices. $∆f>0$ indicates that the probability of the asset being at the highest price is greater than the probability of it being at the lowest price. $∆f<0$ indicates that the probability of the asset being at the lowest price exceeds the probability of it being at the highest price.

4. Empirical Analysis

4.1. Overall Analysis

This study takes daily closing prices in the gold spot market as empirical subjects to investigate the volatility of prices and returns in China’s gold spot market under major events, as seen in Figure 1 and Figure 2. The data span from 26 January 2011 to 31 July 2024. During this period, the price of gold spot experienced several fluctuations. From 2011 to 2013, gold prices were relatively high, but they declined after 2013. Gold prices in China began to rise again in 2016. After a slight increase in 2016, the price of gold spot gradually stabilized. The price remained relatively stable until the second half of 2018, before the onset of US–China trade frictions. Since the second half of 2018, due to multiple instances of US–China trade frictions, the price of gold spot has significantly increased. By the end of 2019, the novel coronavirus emerged in China and gradually spread globally, causing significant fluctuations in the price of gold spot. Initially, the price maintained its previous upward trend, rising to its highest level in nearly seven years before falling back. After a slight decrease, it rose again and gradually stabilized. Against this backdrop, the conflict between Russia and Ukraine escalated, culminating in a full-scale war in February 2022. Influenced by the war, the price of gold spot had continued to rise, reaching its highest point in nearly a decade and continuing to increase.

Table 1. Descriptive statistical of gold spot from 26 January 2011 to 31 July 2024.

.	Number	Mean	Std	Max	Min
Price	3273	295.0981	29.58513	359.04	261.5
Return	3272	2.02 × 10−4	0.009224	0.05189	−0.0947

gives the statistical information on gold prices and returns. It is shown that the return series exhibits considerable volatility, with a maximum value of 0.0519 and a minimum value of −0.0947.

The market efficiency can be analyzed using the Hurst index. As shown in Figure 3, when q = 2, the Hurst exponent for gold spot is 0.4920, which is less than 0.5, indicating that during this period, the gold spot market is anti-persistence. The gold spot market has a certain predictability, i.e., if prices increased in the past, it can be predicted that they will increase in the future as well, and vice versa.

The generalized Hurst index of gold spot is provided in Table 1. It is observed that when q = −6, H(q) is 0.6879, indicating significant persistent characteristics when small fluctuations dominate the return series. When q = 6, H(q) is 0.4045, this indicates significant anti-persistent characteristics when large fluctuations dominate the return series. From

Table 2. Multifractal parameters of gold spot from 26 January 2011 to 31 July 2024.

q	H(q)	α	f(α)
−6	0.6879	0.8010	0.3215
−5	0.6672	0.7786	0.4429
−4	0.6429	0.7441	0.5951
−3	0.6160	0.6963	0.7590
−2	0.5884	0.6398	0.8972
−1	0.5623	0.5846	0.9777
0	0.5384	0.5361	1.0000
1	0.5155	0.4901	0.9746
2	0.4920	0.4415	0.8990
3	0.4677	0.3923	0.7738
4	0.4440	0.3511	0.6283
5	0.4226	0.3225	0.4994
6	0.4045	0.3046	0.4006

and Figure 4, it can be seen that as q varies from −6 to 6, the generalized Hurst exponent H(q) of gold spot returns exhibits a nonlinear decreasing relationship with q. Additionally, from the scaling exponent graph, i.e., Figure 5, the exponent τ(q) is a monotonically increasing concave function of q, showing a pronounced nonlinear relationship with q. All these observations indicate that the returns of gold spot exhibit multifractal characteristics at this time. The multifractal spectrum reflects the fractal dimension of the singular index α. From Figure 5, it can be seen that the multifractal spectrum overall exhibits a bell-shaped curve with a wide distribution range. The singularity index α is not a constant single value, whose maximum value is 0.8010 and minimum value is 0.3046. Therefore, the width of the multifractal spectrum ∆α = 0.4964 > 0 indicates large fluctuations in gold spot returns. The function f(α) varies with the singularity index α, f(α_min) = 0.4006 and f(α_max) = 0.3215, with ∆f(α) > 0, suggesting a higher probability of occurrence of high prices in gold spot returns. Both aspects indicate significant market volatility and higher risk, further confirming the multifractal nature of the gold spot market.

4.2. Segmentation Studies

Figure 1 and Figure 2 show that the price and return of gold spot market fluctuate greatly, which are correlated with the occurrence of a series of major international events such as the US–China trade friction, the outbreak of the COVID-19 pandemic, and the Russia–Ukraine conflict. Therefore, based on the price trends of the gold spot market combined with the occurrence of major events, segmented studies can be conducted to analyze the effectiveness and complex characteristics of the gold spot market under different major events.

On 22 March 2018, U.S. President Donald Trump signed an order at the White House to impose tariffs on Chinese products exported to the United States. And then the United States imposed a 25% tariff on approximately $34 billion worth of goods imported from China, including automobiles and aircraft parts. Shortly afterward, China took corresponding countermeasures, officially starting the US–China trade war. The trade war had a significant impact on both countries. On the one hand, for China, US sanctions in terms of tariffs and technology could reduce investors’ confidence in China’s economic development, leading them to invest in relatively more stable financial products. On the other hand, for the United States, the increased tariffs on Chinese imports also led to higher prices for related goods. Excessive inflation in the US dollar could lead to its devaluation. As a result, investors often turn to gold spot and future markets, which are considered higher-value preservation investments. This shift is one of the main reasons for the rise in gold spot prices during this period. At the end of 2019, the novel coronavirus emerged in China, affecting its economic and social development. Subsequently, the virus spread globally, leading to a pandemic that had negative impacts on economies and societies worldwide. Global output, consumption, and investment decreased, international trade was restricted, and industries suffered significant losses. So, investor confidence plummeted while risk aversion rose. Investors increasingly turned to purchasing gold as a hedge against uncertainty. Many countries implemented various monetary and fiscal policies to stimulate their economies. For instance, the United States implemented multiple interest rate cuts and quantitative easing measures, while China reduced taxes and fees and stabilized prices. Against this backdrop, investor confidence gradually returned, and assets were redirected to other financial products, causing the price of gold to decline. In February 2022, the full-scale conflict between Russia and Ukraine erupted, accompanied by sanctions from multiple countries against Russia and retaliatory actions from Russia. During this period, investor risk aversion continued to increase. Some countries also increased their gold reserves, causing the price of gold spot in the market to rise steadily, reaching historical highs.

Based on this, this paper divides the data into three stages according to major events that occurred. The first stage is from 26 January 2011 to 15 January 2020. During this period, under the influence of the US–China trade war, the price of gold spot was on the rise. On 15 January 2020, China and the United States officially signed the phase one foreign trade agreement. The second stage is from 16 January 2020 to 23 February 2022. In this period, the price of gold spot fluctuated significantly. The COVID-19 pandemic and the economic policies implemented by various countries in response to the pandemic’s impact on the economic situation were key factors influencing gold spot prices. The third stage is from 24 February 2022 to 31 July 2024. In this period, the price of gold spot showed an upward trend. On 24 February 2022, due to NATO’s eastward expansion and the Donbas conflict, Putin announced the launch of a “special military operation” aimed at demilitarizing Ukraine, marking the official outbreak of the Russia–Ukraine conflict. The reason is that the stage was characterized by post-pandemic recovery and the impact of the Russia–Ukraine war, leading to increased investor preference for high-value preservation investment products and a surge in demand for gold.

4.3. Phase Analysis under Different Events

4.3.1. The US–China Trade War

The first stage spans from 22 March 2018 to 15 January 2020. From the price trend in Figure 6, it can be seen that during this stage, the price of gold spot initially experienced a significant rise, reaching a peak of 359.04 before starting to decline slightly. The return of gold spot market prices fluctuated minimally before May 2019, but after May 2019, the return experienced significant volatility, as seen in Figure 7.

The generalized Hurst index is used to analyze the market efficiency. In Figure 8, when $q=2$, the Hurst index of gold spot at that time is 0.4885. This indicates that the market is in a state of anti-persistence, suggesting that market trading efficiency needs further improvement. According to the Hurst index, the current market has not yet reached efficiency, and investors can model the return series using historical information to predict future prices and thereby achieve additional gains.

According to

Table 3. Multifractal parameters of gold spot from 22 March 2018 to 15 January 2020.

q	H(q)	α	f(α)
−6	0.6507	0.7441	0.4393
−5	0.6333	0.7280	0.5268
−4	0.6124	0.7018	0.6424
−3	0.5883	0.6605	0.7834
−2	0.5642	0.6062	0.9159
−1	0.5449	0.5592	0.9857
0	0.5301	0.5286	1.0000
1	0.5124	0.4888	0.9765
2	0.4885	0.4341	0.8911
3	0.4625	0.3843	0.7654
4	0.4388	0.3498	0.6442
5	0.4189	0.3286	0.5486
6	0.4028	0.3160	0.4788

and Figure 9, when $q=-6$, $H\left(q\right)=0.7441$, indicating that the positive persistence of small fluctuations is stronger during this stage. When q = 6, H(q) = 0.4028, reflecting a reverse persistence feature dominated by large fluctuations. Table 3 shows that as q varies from −6 to 6, the generalized Hurst exponent H(q) of gold spot returns exhibits a nonlinear decreasing relationship with q. According to the scaling exponent curve, the exponent τ(q) is a convex function of q that strictly increases monotonically. The nonlinear relationship between τ(q) and q suggests that gold spot returns possess multifractal characteristics.

According to the multifractal spectrum, which is displayed in Figure 10, the f(α) curve shows a wide opening degree resembling a bell shape overall. The range of variation for the singularity exponent α is significant, with α ranging from a maximum of 0.7441 to a minimum of 0.3160. The width of the multifractal spectrum ∆α = 0.4282 is greater than 0. The value of $∆\alpha$ in the first stage is less than the overall value of $∆\alpha$, indicating that during this stage, the volatility of returns is weaker. The escalating trade friction between China and the United States has intensified the complexity of the gold spot market.

The function $f\left(\alpha \right)$ changes with variations in the singularity exponent α, with $f\left({\alpha }_{min}\right)=0.4788$ and $f\left({\alpha }_{max}\right)=0.4393$, and $∆f\left(\alpha \right)<0$. This indicates that during this stage, gold spot returns frequently exhibit lower values. This observation correlates with economic market turbulence amid US-China trade tensions, reflecting the immaturity of the gold spot market development under these conditions. The significant market volatility and higher risk further demonstrate the multifractal nature of the gold spot market.

4.3.2. The COVID-19 Pandemic

Phase 2 spans from 16 January 2020 to 23 February 2022. During this period, the price of gold spot experienced multiple fluctuations, as seen in Figure 11 and Figure 12. Initially, the price surged significantly, reaching a peak of 446.48. Subsequently, there was a sharp decline to 331.74. Afterward, there was a minor increase followed by several small fluctuations, eventually stabilizing at a relatively steady level.

Figure 13 shows that the Hurst index $H\left(2\right)$ of gold spot is 0.3852, which is much less than 0.5, indicating that the market has not reached weak efficiency, and the market is likely to be predicted. During this phase, the return rate of gold spot exhibits anti-persistence, implying that it will have a downward trend after the price rises, the price will rise after a downward trend, and vice versa.

According to

Table 4. Multifractal parameters of gold spot from 16 January 2020 to 23 February 2022.

q	H(q)	α	f(α)
−6	0.6305	0.7074	0.5390
−5	0.6162	0.6953	0.6042
−4	0.5982	0.6780	0.6809
−3	0.5754	0.6496	0.7774
−2	0.5481	0.6031	0.8900
−1	0.5182	0.5465	0.9717
0	0.4840	0.4801	1.0000
1	0.4404	0.3852	0.9448
2	0.3852	0.2591	0.7477
3	0.3240	0.1363	0.4369
4	0.2667	0.0518	0.1403
5	0.2190	0.0055	−0.0675
6	0.1815	−0.0169	−0.1905

when q = −6, H(q) = 0.6305, indicating stronger positive persistence in small fluctuations during this phase. When q = 6, H(q) = 0.1815, which is much lower than the overall phase, i.e., H(q) = 0.4045, highlighting more significant anti-persistence in large fluctuations for this phase. This is consistent with the economic environment during the pandemic. During the pandemic, investor sentiment is highly susceptible to external conditions, leading to large fluctuations in gold prices, with significant ups and downs. It also can be observed from Figure 14 that as q varies from −6 to 6, the generalized Hurst exponent H(q) of gold spot returns exhibits a nonlinear relationship with q. According to Figure 15, the scaling exponent τ(q) is a monotonically increasing convex function of q, demonstrating a nonlinear relationship. Therefore, gold spot returns exhibit multifractal characteristics.

According to the multifractal spectrum from Figure 15, the f(α) curve shows a significant opening, resembling a bell shape overall. The range of singularities α varies greatly, with a maximum value of 0.7074 and a minimum of −0.0169. The width of the multifractal spectrum Δα = 0.7243 > 0 in this phase is much larger than both the overall width and the first phase, which indicates that during this phase, the volatility of the gold spot market is severely influenced by the COVID-19 pandemic. During this phase, there is a much higher probability of occurrence for the maximum values of gold spot returns compared to the minimum values. The $f\left(\alpha \right)$ varies with the singularityα, where $f\left({\alpha }_{min}\right)=-0.1905$, $f\left({\alpha }_{max}\right)=0.4631, ∆f\left(\alpha \right)>0$, indicating that during this phase, there is a much higher likelihood of low values of gold spot returns compared to high values. This phase is influenced by the COVID-19 pandemic and experienced significant market volatility and higher risk, further demonstrating the multifractal characteristics of the gold spot market. The impacts of the US–China trade friction and the COVID-19 pandemic on market risk in the gold spot market are different. The complexity and risk of the gold market are more significantly affected by the COVID-19 pandemic than by the US–China trade relations.

4.3.3. The Russia–Ukraine War

This phase spans from 24 February 2022 to 31 July 2024. During this phase, gold spot prices experienced significant fluctuations and reached an all-time high of 567.9. The increase in gold spot prices was relatively small before 2023, but after 2023, the rise became significantly steeper and showed a continuing upward trend, as seen in Figure 16 and Figure 17.

From Figure 18, the Hurst exponent H = 0.4155 for gold spot, which is less than 0.5, indicating that the market is anti-persistence, not weak-form efficiency. The Hurst index of this phase is less than both the overall and the US–China trade war phases and slightly higher than the COVID-19 pandemic phase.

According to

Table 5. Multifractal parameters for gold spot from 24 February 2022 to 31 July 2024.

q	H(q)	α	f(α)
−6	0.6766	0.8131	0.1810
−5	0.6509	0.7925	0.2918
−4	0.6192	0.7562	0.4519
−3	0.5817	0.6974	0.6529
−2	0.5410	0.6184	0.8451
−1	0.5015	0.5351	0.9663
0	0.4666	0.4635	1.0000
1	0.4381	0.4106	0.9725
2	0.4155	0.3734	0.9158
3	0.3970	0.3446	0.8427
4	0.3810	0.3197	0.7547
5	0.3668	0.2983	0.6577
6	0.3540	0.2811	0.5624

and Figure 19, when $q=-6,H\left(q\right)=0.6766$, which indicates that the positive persistence is significant when small fluctuations dominate in this stage. When q = 6, H(q) = 0.3540, indicating that under this period, the reverse persistence characteristic is stronger when large fluctuations dominate. As seen from Table 5 and Figure 20, when q varies from −6 to 6, the generalized Hurst exponent H(q) of gold spot returns has a nonlinear relationship with q. From the scale index graph, i.e., Figure 20, it is observed that the exponent τ(q) is a monotonically increasing convex function of q, and τ(q) has a nonlinear relationship with q. Thus, the gold spot returns exhibit multifractal characteristics.

According to the multifractal spectrum, the curve $f\left(\alpha \right)$ has a larger opening degree, an overall bell shape, and a wide range of the singular index $\alpha$. The maximum value of the singular index $\alpha$ is 0.8131, the minimum value is 0.2811, and the width of the multifractal spectrum is $∆\alpha$ = 0.5320 > 0. In this stage, the value $∆\alpha$ is significantly greater than both the overall and US–China trade war phases and lower than the COVID-19 pandemic phase. The magnitude of change in $\alpha$ is large, revealing a high volatility in returns. At this time, the volatility in the gold spot market is severe, approaching exceeding the intensity of the overall and the first phases. The probability of the minimum return on gold spot is much higher than that of the maximum return. The function $f\left(\alpha \right)$ changes with the singularity index α, where $f\left({\alpha }_{min}\right)=0.5624$,$f\left({\alpha }_{max}\right)=0.1810, ∆f\left(\alpha \right)<0$. This indicates that during this phase, the frequency of the minimum returns on gold spot is slightly higher than that of the maximum returns. This phase is influenced by the Russia–Ukraine war, market volatility increased, and risk is high, further demonstrating the multifractal characteristics of the gold spot market. It is evident that the impacts of the US–China trade friction, the COVID-19 pandemic, and the Russia–Ukraine war on the risk of the gold spot market are quite similar. All three events increased the difference between the maximum and minimum returns, raising the risk in the overall phase.

4.3.4. A Comparative Analysis of the Overall and Stages

Table 6. Effectiveness and complexity overall and across the three phases of the Chinese gold market.

	Overall	US-China Trade War	COVID-19 Pandemic	Russia-Ukraine War
H (2)	0.4920	0.4885	0.3852	0.4155
Effectiveness	Anti-persistence	Anti-persistence	Anti-persistence	Anti-persistence
$∆\alpha$	0.4964	0.4281	0.7245	0.5320
Complexity and risk	Have	Have	Have	Have

provides the effectiveness, complexity, and overall risk across the three phases. From Table 6, comparing the generalized Hurst exponent of the overall period and three phases, when q = 2, the generalized Hurst exponent for the overall period is 0.4920. For the first, second, and third phases, it is 0.4885, 0.3852, and 0.4155, respectively. It is evident that the gold spot markets of the overall and three stages under different major events are not weak-form efficiency. The Hurst index during the COVID-19 pandemic is the smallest among all stages, which indicates that the intensity of anti-persistence is the greatest. The intensity of the anti-persistence Russia–Ukraine War is higher than the overall and US–China trade war phases. This suggests that significant geopolitical events can moderately affect the effectiveness of the gold spot market. However, unpredictable major events that threaten public safety, such as the COVID-19 pandemic, are more likely to have a greater impact on the effectiveness of gold spot. The shutdown caused by the epidemic, the policies adopted by various countries to stimulate the economy, and the irrational behavior of investors have greatly weakened the effectiveness of the market, preventing the effective allocation of resources from being achieved.

The Δα between the overall stage and the three stages is different. The Δα for the overall time period is 0.4964; for the first stage, it is 0.4281; for the second stage, it is 0.7245; and for the third stage, it is 0.5320. It is evident that the gold spot market exhibits a complex multifractal feature. This complexity indicates higher risks, as major events can influence market complexity to varying degrees, thereby increasing market risk. In the COVID-19 pandemic stage, Δα is the highest, with the gold spot market exhibiting the greatest fluctuations between maximum and minimum returns, indicating significant multifractal characteristics and the highest market risk. The Δα of the Russia–Ukraine war phase is higher than the overall and US–China trade war phases, suggesting that the impacts of the Russia–Ukraine conflict on the riskiness of the gold spot market are relatively strong. Both above events enhance the riskiness of the gold spot market, leading to increased investment risk for investors. This finding is consistent with Drake’s (2021) empirical research on the 2007–2009 economic crises and the 2019 COVID-19 pandemic period, which does not support gold as a safe haven asset [31]. As seen in Table 6, it can be observed that the stronger the anti-persistence, the greater the gold market risk.

In order to compare the Chinese and foreign gold markets, given the availability of data and the impact of the US–China trade war, we used MFDFA to analyze the American gold market, particularly comparing the characteristics of the two markets under three major events. Based on data availability, the American gold price data ranges from 6 June 2017 to 31 July 2024 is collected. The time periods for the three major events, namely the US–China trade war, the COVID-19 pandemic, and the Russia–Ukraine war, remain unchanged. The results are shown in

Table 7. Effectiveness and complexity overall and across the three phases of the American gold market.

	Overall	US–China Trade War	COVID-19 Pandemic	Russia–Ukraine War
H (2)	0.3950	0.4102	0.3819	0.3934
Effectiveness	Anti-persistence	Anti-persistence	Anti-persistence	Anti-persistence
$∆\alpha$	0.7970	0.7732	0.9985	0.7780
Complexity and risk	Have	Have	Have	Have

. As can be seen from Table 7, the American gold market also exhibits anti-persistence, both in the overall period and during the three major events. Furthermore, the intensity of anti-persistence during the COVID-19 pandemic is the highest, and the corresponding market complexity and risk are also the strongest among the three major events. Therefore, the gold markets of the two countries show similarities, indicating that different national gold markets are strongly interconnected in the international market and that major events can impact the financial markets of different countries.

4.3.5. Discussion and Suggestions

The aim of this study is to analyze the gold market’s efficiency, complexity, and risks. The following suggestions and countermeasures are put forward for China’s gold spot market:

As the primary market participants, investors should strengthen their knowledge of financial products such as spot, recognize the importance of diversified investments, and reasonably diversify investments to reduce risks. This prevents blind investments from deteriorating market efficiency and fully leverages the market’s resource allocation function. There are many investment products available in the gold market, such as relatively stable gold bars and coins (physical gold) and investment methods with both risk and reward, like gold spot and gold stocks. Each product has its own advantages and disadvantages. Investors should fully utilize the characteristics of different gold investment products, considering market risk, price fluctuation risk, policy risk, and their own risk preferences comprehensively. They can choose an appropriate gold investment portfolio to reasonably control risk, avoiding putting all their eggs in one basket.

As the regulator of the gold market, the government should fully utilize its supervisory functions to improve market liquidity, perfect the market information transmission system, reduce transaction costs and various fees, and effectively lower market risks. This process not only enhances the efficiency and precision of resource allocation but also further stimulates the active participation of rational investors in the market, collectively promoting the healthy and efficient development of China’s financial market. Additionally, risk managers should monitor market dynamics in real time, respond proactively to market performance, and formulate reasonable policies to control risks. Meanwhile, government authorities should strengthen market supervision and refine and improve the trading and disciplinary mechanisms of the gold spot market. By accurately identifying, rigorously investigating, and resolutely combating various illegal and irregular market activities, the regulators can create a more standardized and efficient development environment for China’s gold spot market, thereby ensuring its stable and orderly continuous growth.

Based on the empirical analysis results, the specific recommendations are as follows: the empirical results show that the gold market exhibits anti-persistence both overall and under three major events, indicating market predictability. This is especially true for the market during the COVID-19 pandemic, where anti-persistence is very strong; that is, the stronger the previous rise in gold prices, the stronger the subsequent decline. Therefore, for investors, there are opportunities to trade gold based on major events. However, the study also found that the poorer the market efficiency, the greater the risk. Hence, when investing in gold, it is crucial to be mindful of the risks.

For regulators, since the gold market has not achieved weak efficiency, particularly under the background of major events, the market’s efficiency is even weaker. Therefore, regulators should improve the information disclosure system to combat insider trading, regulate market investment behavior, and enhance market efficiency. Additionally, during major events, market regulators should establish risk management mechanisms, improve the regulatory framework for the gold market, and strengthen risk prevention capabilities to cope with market fluctuations.

5. Conclusions

Based on the gold spot price data from January 2014 to April 2024 under the background of some major events, this paper uses the multifractal detrended analysis method (MFDFA) to investigate the effectiveness and complexity of the gold spot market. The results show that the return of gold spot in each phase exhibits changing trends and possesses multifractal characteristics.

Overall, except for the second phase, the gold spot market in other phases is generally close to being weakly efficient. And the first phase is very close to weak efficiency. Additionally, the gold spot market exhibits multifractal characteristics, with significant market fluctuations and high risk. Currently, China’s gold spot market is not yet a mature and highly efficient capital market. It requires joint efforts from all market participants to enhance investor management, strengthen the information disclosure system, and continuously improve market mechanisms.

This paper utilizes MFDFA to study the single market of gold. However, during some major events, many financial markets influence each other, and only analyzing the gold market would lack the consideration of external factors. In the future, we will use MF-DCCA to investigate the connections between the gold market and the exchange rate, stock, and energy markets. Additionally, the asymmetry of the gold market during the rising, falling, and oscillating phases also needs to be analyzed.