Research Article  Open Access
Emmanuel AsafoAdjei, Siaw Frimpong, Peterson Owusu Junior, Anokye Mohammed Adam, Ebenezer Boateng, Robert Ofori Abosompim, "MultiFrequency Information Flows between Global Commodities and Uncertainties: Evidence from COVID19 Pandemic", Complexity, vol. 2022, Article ID 6499876, 32 pages, 2022. https://doi.org/10.1155/2022/6499876
MultiFrequency Information Flows between Global Commodities and Uncertainties: Evidence from COVID19 Pandemic
Abstract
Owing to the adverse impact of the COVID19 pandemic on world economies, it is expected that information flows between commodities and uncertainties have been transformed. Accordingly, the resulting twisted risk among commodities and related uncertainties is presumed to rise during stressed market conditions. Therefore, investors feel pressured to find safe haven investments during the pandemic. For this reason, we model a mixture of asymmetric and nonlinear bidirectional causality between global commodities and uncertainties at different frequencies through the information flow theory. Consequently, we utilise the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and the Rényi effective transfer entropy techniques to establish the dynamic flow of information. The intrinsic mode functions (IMFs) from the CEEMDAN are carefully extracted into multifrequencies through cluster analysis to reconstruct the series into high, medium, and low frequencies in addition to the residue. We utilise daily data from December 31^{st}, 2019, to March 31^{st}, 2021, to provide insights into the COVID19 pandemic. The correlation coefficients and variances demonstrate that the high frequency (IMFs 1–4) which measures the shortterm dynamics is the dominant frequency, suggesting shortlived market fluctuations relative to real economic growth for institutional investors. Moreover, outcomes from the multifrequency entropy indicate a negative bidirectional causality of information flow between global commodities and uncertainties, especially in the long term. Generally, the findings present pertinent inferences for portfolio diversification, policy decisions, and risk management schemes for global commodities and markets volatilities. We, therefore, advocate that market volatilities act as effective hedges for global commodities, and they clearly act as balancing assets rather than substitutes in the longterm dynamics of the COVID19 pandemic. Investors who delayed in investing within financial markets of commodities and market volatilities are likely to minimise their portfolio risks.
1. Introduction
Commodities have developed as one of the most important categories of assets in the global economy [1]. From the beginning of the late 10^{th} century, commodity investing has attracted the attention of researchers, policy makers, and investors. Commodities are mainly categorised into metals, energy, and agricultural products [2]. Despite the differences in their categorisations, they are likely to offer diversification, safe haven, or hedge benefits [3–5]. Specifically, among the family of metals, precious metals have induced the attention of academicians, specifically, gold [6]. Gold acts as a dominant safe haven asset [6, 7], but very little is known about the safe haven properties of other metals in times of severe economic and financial havoc [6]. The same can be said of agricultural and energy commodities. Notwithstanding, Ahmed and Sarkodie [8] indicated that commodities depict high probability to remain in low volatility regime than in high volatility regime. They demonstrated that precious metals and agricultural commodities display less inverse response to uncertainties than energy. It can, therefore, be inferred that commodities display high likelihoods of asymmetric dynamics among themselves [3, 9, 10].
Commodities are not only considered for their fundamental physical usage but also considered as a potential hedging instrument during uncertainties. Nonetheless, commodities are likely to experience similar chaotic risk as other assets, thereby plummeting their prices. With reference to the 20072008 global financial crisis, there have been major uncertainties in the financial and economic setting, including financial contagion risk [11, 12], economic downturns [13, 14], political turmoil [15, 16], Brexit [17, 18], and cryptocurrency crashes which in turn spread contagion and weaken financial stability [19]. These disturbances have an adverse impact on commodities, thereby plunging their hedging or safe haven potentials [1, 6, 8, 11–18].
In addition to these disturbances, the emergence of the COVID19 pandemic has induced many empirical studies on the globe, including its impact on health [20–23], food prices [24], the nexus between equities and cryptocurrencies [25], commodities [8, 26], and major world markets [27, 28]. It can be analysed from these studies that the impact of the COVID19 pandemic has disrupted most economic activities including financial markets of which commodities are no exception.
The contagious impact of COVID19 on markets does not substantially deviate from the efficient market hypothesis (EMH) [29, 30]. Thus, relevant information about the COVID19 pandemic may largely reflect in ascertaining current prices of financial assets. The rippling effect would be a fall in market prices over time. On the other hand, the heterogeneous and adaptiveness of market participants across time, market overreaction, mean reversion, excessive volatility, and all other market anomalies provide support to investigating the commodities and uncertainties’ information flow dynamics during the COVID19 pandemic. Hence, we are curious to ascertain the flow of information between important commodities and uncertainties during the COVID19 pandemic. We do this to assess the extent of immunity of the commodities to uncertainties in times of economic shocks.
The exegesis of the COVID19 pandemic on commodities has substantially been provided by prior studies with varying outcomes [8, 26–28]. This is partly due to the behavioural intentions of investors which is not the same across time, with fluctuating economic conditions which contradict the EMH. As a result, the asymmetric and timebased varying behaviours of investors are carefully supported by the heterogeneous market hypothesis (HMH) [31] and the adaptive market hypothesis (AMH) [32]. The HMH provides that the numerous market participants take their investment decisions on dissimilar time horizons in line with their risk and return preferences by making reference to their past and current news. Again, the AMH states that markets evolve–due to events and structural changes, adapt–and market efficiency varies in degree at different times. In this study, we employ intrinsic time which concurs with time scales of short, medium, and long term to account for time horizons.
Also, we consider the hypothetical advancement of Owusu Junior et al. [28, p. 2] on the competitive market hypothesis (CMH) which argues that “in part, the intensity of information flows and spillover between markets of the same and differing asset classes are exacerbated by rational, albeit irrational investors’ relentless search for competing rewards and risks to satisfy the portfolio goals.” As a result, the intensity of information flows between markets (similar and dissimilar) may lead to high uncertainties to which individual financial markets are susceptible. This is in line with the financial instability of Minsky [33–35] and the asymmetric volatility dynamics.
The theoretical exposition of Minsky [33–35] on financial instability provides a linkage between financial market fragility and endogenous speculative investment bubbles. This hypothesis claims that economic tranquillity and stability are not selfsustaining. Accordingly, stability could lead to more optimism which eventually leads to more borrowing in financial markets. Over time, there is a transformation from a stable financial system to a fragile system. Thus, consequently, stable and booming markets drive blindness for increasing risks [36]. The impact may however not be instantaneous but differed even to periods of existing markets stress such as the COVID19 pandemic which may aggravate the overall market risks. We take cognisance from the dynamics of the preCOVID19 pandemic shock transmissions from stable and booming markets which may drive blindness for increasing future risks and the impact of the current COVID19 pandemic shocks. We institute that asset price response to information may heed from past (due to time delay mechanism and accumulation effect) as well as current information regarding market inefficiency.
In addition, arguments on asymmetric volatility [37] in the discussion of uncertainties and commodities markets cannot go unnoticed. This is because fluctuations in market volatilities influence investors’ portfolio choices either by altering the tradeoff between risk and return or their predictions of future market performance. According to Chen [38], investors’ desire to hedge against market volatility because rising volatility does not incentivize investment opportunities. Consequently, phases of high volatility tend to correspond to drawdowns in markets which may minimise investors’ confidence [39].
Furthermore, Benthall [40] advocates that information flows are causal flows located in the context of other causal linkages. The information flow theory builds on the philosophy of Dretske [41] and the statistics of Pearl [42]. The mathematics of probability and statistics has made it possible to quantify the information flow between variables. Intuitively, reciprocal information exists when two random variables are linked in such a way that one variable can learn about the state of the other from observation of the other [40].
We draw insights from the aforesaid theoretical and hypothetical advancements to provide that the competitiveness of markets intensifies the flow of information among them and the stable and booming markets drive blindness for increasing risks and eventually result in an asymmetric volatility information flow to markets. The dynamics of price response to shocks may not be instantaneous due to market friction [43]. In frictionless capital markets with complete information and rational investors, asset prices adjust to new information immediately and completely [44]. However, information imperfections potentially hinder timely price discovery and are associated with delayed stock price adjustment to information [44, 45]. According to Hou and Moskowitz [43], the most delayed firms grasp a large return premium not expounded by size, liquidity, or microstructure effects. They indicate further that delay captures part of the size effect, idiosyncratic risk is priced only among the most delayed firms, and earning drift is monotonically increasing in delay.
As a result, the relentlessness of market frictions affecting an asset contingent on the delay with which its price responds to information during stressed conditions as well as shocks from past markets dynamics may offer diversification potentials in the long term. The time delay mechanism has been illustrated within commodity markets by prior studies [46, 47]. The delayed effect of prices response to shocks through uncertainties on individual markets as a result of intensity of information flows between markets which amplifies market risks, and the impact of other external shocks place the empirical analysis in perspective. We expect diversification potentials to increase monotonically from the short to long terms (delay in market dynamics) in times of stressed conditions. These complex analogies are reflected in what we call “the delayed volatility of market competitiveness and external shocks (DVMCES)” phenomenon. The market competitiveness can be analysed from either same or different class of assets.
We therefore employ five uncertainty indices which include Economic Policy Uncertainty (EPU), Global Volatility Index (Gvolatility), Cryptocurrency Volatility Index (VCRIX), Chicago Board Options Exchange (CBOE), Volatility Index (VIX), and CBOE Crude Oil Volatility Index (OVX). Gvolatility represents volatility in all financial markets, whereas the VIX is a proxy for investor fear and expectations in the equity markets. Also, the VCRIX is utilised in this study due to the cryptocurrency crashes which in turn spread contagion and weaken financial stability [19]. In addition, we consider the OVX which is one of the most important volatility indices in the commodity markets [48–50]. These four uncertainty indices are employed to investigate whether the competitiveness of markets would either transmit volatility from alternative markets to other markets or shocks from the other markets transmit significant information to the volatilities of alternative markets.
Due to the world uncertainty and cotemporary conflicts, there is an increasing body of uncertaintygenerating policies that influence economic policy and financial decisions [51]. The EPU index includes a range of concerns, for instance, conflicts in regulations, conflicts over inequality of income distribution, and fluctuations in global prices, to mention a few, that occur around the globe. The creation of the EPU index has therefore induced several empirical studies [6, 52, 53]. From the points so far discussed, we rigorously examine the DVMCES phenomenon in the context of global commodities and uncertainties. This can, however, be extended to other markets.
Empirical studies on the flow of information between uncertainties and commodities during the COVID19 pandemic at diverse intrinsic time are underdeveloped. This investigation is necessary because different commodities are distinguished by different time responses to shocks in the market [54]. An avalanche of studies have examined the spillover effects or nexus between commodities and uncertainties [8, 55, 56]. Studies have been conducted on the volatility transmission in precious metal markets [57, 58], energy markets [59, 60], agricultural commodities [61], regime switching effect of the COVID19 pandemic, and EPU on three commodity categories—metals, energy, and agriculture [8]. However, these studies did not consider the flow of information at diverse intrinsic times during the COVID19 pandemic. Also, little is known about the flow of information between global commodities and the five important uncertainties—EPU, Gvolatility, VCRIX, VIX, and OVX, during the COVID19 pandemic. On the other hand, the few empirical studies that come close to investigating the information flow between commodities and uncertainties [59] did not employ the Rényi transfer entropy at various intrinsic times which corresponds to the stylised facts of financial returns. In addition, most studies have not considered similarities between commodities or uncertainty indices (except GEPU) which is necessary for revealing the level of efficiency or heterogeneity within the markets at specific or diverse intrinsic times.
Accordingly, empirical studies on the commodities and uncertainties nexus have warranted methodologies such as linear and nonparametric causality tests [62], bootstrap causality test and the timevarying approach [57], feasible quasigeneralized least squares estimator [55], causality in variance test and impulse response functions [61], entropybased wavelet analysis [59], timevarying parameter vector autoregression model [60], and GAS and GARCH modelling of precious metals in addition to the Hansen et al. model confidence set in ranking superior set model [58]. None of these methods considered multifrequencydependent entropy approach which quantifies information from a probability density function in the short, medium, and long terms.
Our study departs from extant literature by first employing the complete ensemble empirical mode decomposition with adaptive Noise (CEEMDAN), offered by Torres et al. [63] to solve the problem of mode mixing caused by the empirical mode decomposition (EMD) method as well as the inability of the EEMD to completely eliminate Gaussian white noise after signal reconstruction [64]. Mode mixing, according to Wu and Huang [65], is defined as any IMF consisting of oscillations of intensely disparate amplitude, mostly caused by intermittency of the driving mechanism. Thus, the physical meaning of an IMF can cease by itself, indicating falsely that there may be diverse physical processes embodied in a mode.
The CEEMDAN is a suitable method for sampling and dealing with the noise of signals and significantly attenuates the frequency aliasing problem that may occur with EMD and EEMD as developed by Huang et al. [66] and Wu and Huang [67], respectively. The CEEMDAN method realizes the continuity in frequency between adjacent scales by adding a certain white noise [68]. It uses the original series as the goal of IMF sifting and completely solves the two constraints—inconsistency in the number of decomposition scales and some inevitable error which exists between the reconstructed and original signals [63, 68]. Through the CEEMDAN, modes are reasonably extracted nonrecursively, which makes it a fully intrinsic, adaptive, and quasiorthogonal decomposition method [63].
The CEEMDAN meticulously decomposes input signals into their major modes, known as intrinsic mode functions (IMFs), which reproduce the input signal but with varying sparsity qualities. Specifically, in the context of this study, the IMFs represent short, medium, and longterm periods [28]. The CEEMDAN is purposely employed in this study to minimise noise in the data. Information that misrepresents unpretentious core patterns is referred to as noise. Small price corrections in the market, as well as price variations that distort the broader trend, are examples of noise in the financial markets. This suggests that market noise might make it difficult for investors to tell what is driving a trend and whether it is fundamentally changing or simply experiencing shortterm volatility. This is in line with the HMH [31] and the AMH [32].
Corollary to the CEEMDAN, we present the effective transfer entropy that occurs from the formulation of conditional related information [69]. Transfer entropy quantifies the reduction in uncertainty especially when conditioned on past values in forecasting variables and thus makes it easier to model statistical causality between variables in a natural phenomenon [28, 40, 70]. Consequently, the amount of information that flows between commodities and volatilities can be quantified using transfer entropy. Therefore, the CEEMDANbased entropy would provide an asymmetric method to measure the flow of information, after accurately decomposing the time series data into their IMFs. This approach is lacking in prior studies on commodities and uncertainties.
Our study offers contributions to literature in many ways. First, we adopt the multifrequency CEEMDANbased entropy to examine the information flow between commodities and uncertainties. We follow Adam et al. [71] to capture the IMFs into high, medium, and low frequencies, in addition to the residue using cluster analysis to account for only four multifrequencies. This is done to carefully extract the four dynamics of frequencies in financial time series [71, 72]. This is enriched with detailed information for decision making while aggregating similar IMFs based on mean periods to minimise cumbersome analysis. Second, we assess the similarities among the commodities and uncertainty indices through the Pearson correlation and Kendall taub coefficients from the outcome of the cluster analysis [71, 72]. Third, we consider the Rényian transfer entropy (RTE) to deal with issues of nonlinearity, nonstationarity, and asymmetry which may occasion a deterministic system to chaos [73]. In addition, the RTE is a loglikelihood ratio transfer entropy which quantifies information from a probability density function. The RTE is specifically used in this study instead of the Shannon entropy to account for tail events associated with pricing relevant financial information in times of COVID19. Consequently, it is extreme event rather than observation in the centre that comes to light when information flow is utilised [25, 28, 74].
Fourth, since multifrequency analysis is pertinent in this study, we utilise a relatively long time period of COVID19, which has caused havoc on financial markets [28, 75]. This would offer better discernments and indulgence about the diversification potentials of commodities in times of shocks [76]. Fifth, we utilise five uncertainties relevant to commodities—EPU, Gvolatility, VCRIX, VIX, and OVX. Fifth, we provide a rigorous analysis of 20 commodities categorised into metals, energy, and agriculture. Seventh, the extent to which uncertainty indices can hedge against fluctuations in commodities markets is adequately investigated in this study. We further examine the DVMCES phenomenon which has never been considered by prior studies on information flows [25, 27, 28, 69, 73]. The outcome of the study will bolster confidence in existing investors within these markets to either give up part or all of their investments or ensure their effective management in times of shocks. The study will assist investors in making optimal portfolios, considering the overwhelming global financial influence of the COVID19 pandemic [56]. Accordingly, the current study, to the best of our knowledge, is among the very few empirical studies that extensively assess information flow between global commodities and uncertainties, while drawing insights from the COVID19 pandemic.
Our empirical analysis revealed that the correlation coefficients and variances demonstrate that the high frequency (IMFs 1–4) which measures the shortterm dynamics is the dominant frequency. Findings from the multifrequency entropy indicate a negative bidirectional causality information transfer between global commodities and uncertainties, especially in the long term. Generally, the findings present pertinent inferences for portfolio diversification, policy decisions, investing risk, and risk management schemes for global commodities and market volatilities. We advocate that investors who delayed in investing within financial markets of commodities and market volatilities during the COVID19 pandemic are most likely to minimise their portfolio risks.
The rest of the study is well thought out as follows. Section 2 contains the study’s methodologies on the CEEMDANbased Rényi transfer entropy, and data sources and description are presented. Section 3 provides analysis of the main results, and theoretical and practical underpinnings are found in Section 4, and the main conclusions are drawn in Section 5.
2. Methodology
2.1. CEEMDAN
The empirical mode decomposition techniques have gained rapid attention by researchers due to their purely datadriven algorithm to separate scales which are exclusive of predefined basis functions, disparate to wavelet decomposition [77]. Thus, in the wavelet decomposition (for instance, the maximal overlap discrete wavelet transform and discrete wavelet transform), a predefined mother wavelet is needed to decompose a signal, and the selection of the mother wavelet is subjective and influential [77]. Nonetheless, the EMD method resorts to scale mixing problem. This problem was solved with the ensemble empirical mode decomposition method (EEMD) developed by Wu and Huang [67] to incorporate a randomly generated white noise series to the original signal. Thankfully, Torres et al. [63] developed the CEEMDAN to solve the residual noise in the reconstructed signals within the EEMD by appending the noise to the residual of prior iteration instead of the original signal [77].
In CEEMDAN, compared to EMD, EEMD, and possibly CEEMD, irrespective of the number of decompositions, the reconstruction error of the signal approaches zero, and the completeness is better. Further, it solves the problem of low decomposition efficiency and saves a great deal of processing power. Again, the output of CEEMDAN follows a Gaussian distribution, so that each IMF follows [78]. This is important because the observed data often describe a set of phenomena which may be of different kinds, i.e., which may include phenomena of different quality [79], and these different qualities presents themselves in quantitative discrepancies in financial time series. The global commodity and uncertainty variables were decomposed into seven IMFs and a residual. This was implemented with the libeemd R package [80]. The application of the algorithm is summarised as follows.
Begin the number of realizations N, noise parameters, index for IMF j = 1.
Perform the EMD for N realizations; , where n refers to the index for realizations; is the white noise series added to the candidate signal; and is the noise parameter for the initial step.
The ensemble mean intrinsic mode functions (IMF) are calculated as
The exclusive first residue can be determined as
Evolve N number of realizations; then, the operator produces mode obtained by EMD.
The final step is to calculate the residue, where :
2.2. Cluster Analysis
The cluster analysis enables us to group the IMFs which we consider in this study as high, medium, and low frequencies. We consider the high, medium, and low frequencies in this study as multifrequencies [71, 72]. The multifrequencies are obtained by observing the mean periods of each IMF. The mean period is the average frequency of each IMF. It is measured as the ratio of the total number of points to the number of peaks [71, 72, 81]. Specifically from the CEEMDAN, the mean period is calculated aswhere the number of peaks (maxima) is obtained through the extrema function [82]. We then sum up the IMFs based on the mean period obtained to categorise them into their respective multifrequencies [81].
2.3. Rényi Transfer Entropy
Before we discuss the Rényi transfer entropy, we present the idea of Shannon entropy as a measure of uncertainty upon which transfer entropy is embedded in information theory [83]. We consider a probability distribution with diverse results of a given experiment . Following Hartley [84], each symbol’s average information is detailed aswhere n denotes number of diverse symbols with respect to the probabilities .
The concept of Shannon entropy was introduced in 1948 by Shannon [85]. It indicates that for a discrete random variable () that has a probability distribution of (), the average number of bits necessary to optimally encode independent draws [83] can be presented as
With the notion of Markov processes, Shannon entropy is aligned with the concept of Kullback–Leibler distance [86] in order to measure the information flow between two time series. We present and as two discrete random variables with corresponding marginal probabilities of and and joint probability , with dynamic structures in line with a stationary Markov process of order () and (). The Markov property signifies that the probability to detect at time in state conditional on the previous observations is . To encode the reflection in , the average bit number required once the ex ante k values are known can be illustrated aswhere (similar in the same respect for process J). In a bivariate perspective as well as relying on the Kullback–Leibler distance [86], information flow from process J to process I is measured by computing the deviation from the generalized Markov property . The Shannon transfer entropy can thus be presented aswhere calculates the information flow from to . Analogously, , as a measure for the information flow from to , can be derived. The main direction of the information flow can be concluded by calculating the difference between and .
Based on the Shannon entropy so far discussed, we present the Rényi transfer entropy [87] which is contingent on a weighting parameter and can be calculated aswith . For , Rényi entropy converges to Shannon entropy. For , thus, low probability events receive more weight, while for , the weights benefit outcomes with a higher initial probability. As a result, Rényi entropy permits to emphasize diverse distribution areas, depending on parameter [70, 83].
Applying the escort distribution [88] with to normalize the weighted distributions, Rényi transfer entropy [86] is derived as
It is worth noting that the Rényi transfer entropy can have negative values. As a result, knowing the history of depicts even greater uncertainty than would otherwise be indicated by only knowing only the history of .
The transfer entropy parameters are biased in small samples [89]. The correction of the bias to calculate the effective transfer entropy iswhere depicts the transfer entropy via a shuffled form of the time series , that is, selecting values at random from the observed time series and realigning them to form a new time series, destroying the time series dependencies of , and not forgetting the statistical dependencies between and . This enjoins to come together to zero with increasing sample size, and any nonzero value of is due to small sample effects.
As a result, repeated shuffling and the average of the shuffled transfer entropy assessments across all replications can be used as a small sample bias estimator. This is subtracted from the Shannon or Rényi transfer entropy estimate to get a biascorrected effective transfer entropy estimate.
Relying on a Markov block bootstrap, the statistical significance of the transfer entropy estimates, as given by equation (12), can be inspected as provided by Dimpfl and Peter [74]. This preserves the dependencies within the variables and but ignores the statistical dependencies between and opposing to shuffling. The distribution of the estimates under the null hypothesis of no information movement is then determined by repeated estimation of transfer entropy. The associated is given by where signifies the simulated distribution’s quantile, which is defined by the transfer entropy estimate [83].
2.4. Data Sources and Description
The study employs 20 daily commodity prices which can be relatively described as aggregated and individual commodities. They include global commodities (Acommodity), global energy (Aenergy), global metals (Ametals), industrial metals (Imetals), Brent, gasoline, heating oil (Htoil), natural gas (Ngas), petroleum, cocoa, coffee, corn, cotton, soybeans, wheat, gold, lead, nickel, palladium, and zinc. We further present five uncertainty indices: the US Economic Policy Uncertainty (EPU), NASDAQ 100 Volatility Target (Gvolatility), Cryptocurrency Volatility Index (VCRIX), Chicago Board Options Exchange (CBOE) Volatility Index (VIX), and CBOE Crude Oil Volatility Index (OVX). The daily data span from December 31^{st}, 2019, to March 31^{st}, 2021, yielding a total of 306 observations after balancing the data. The suggested time frame is chosen to encompass the COVID19 pandemic.
The commodities are carefully selected to include various categorisations of important commodities mostly employed by extant literature in addition to commodities which are less considered in empirical literature. We include both aggregated and individual commodity indices to provide a detailed information flow dynamics with uncertainties during COVID19 pandemic. The variables are selected based on consistent data availability for the chosen period and their importance for investment decisions. We do this to reveal hidden relationship of multifrequency information flow between the commodities and uncertainty indices to establish the DVMCES phenomenon analogous to the competitive market hypothesis [28]. The data on the commodities, Gvolatility, VIX, and OVX, were obtained from investing.com, whereas EPU and VCRIX were obtained from the websites https://www.policyuncertainty.com/index.html [51] and https://data.thecrix.de/data/vcrix.csv, respectively, with the US dollars as the currency value where appropriate. The study was based on daily returns of , where is the incessantly compounded return and and are current index and preceding index correspondingly.
2.5. Preliminary Analysis
Figure 1 provides the timevarying prices and returns of both global commodities (black trends) and uncertainties (red trends). The different colour trends within the plots are presented to enhance identification. It can be observed from the plots that at the early sections of 2020, the prices for all markets trend upwards, after a plunging spike between February, 2020, and May, 2021. That is, the prices of global commodities are experiencing a rapid increase which concur with the assertion made by Zhang et al. [90] of markets rebound later in the COVID19 pandemic since most busineses and economies had learnt how to survive. Thus, the dynamics of most markets have begun to return to normal. Generally, it can be observed from the plots that fluctuations in global commodities are similar which makes analysis of this study during COVID19 highly comparable. Furthermore, the uncertainties display inverse relationships with the global commodities, except the Global Volatility Index, which depicts increasing trend, and possibly the Cryptocurrency Volatility Index. The logreturn plots exhibit volatility clustering as anticipated due to the stylised facts of financial time series [91].
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Table 1 shows the preliminary statistical analysis for the returns series. The negative mean returns indicate the poor performance of financial assets during COVID19 while the positive returns depict markets able to withstand shocks. The negative skewness specifically for the aggregated, agricultural, and metal commodities suggests that investing in these assets should be done with caution since there is a likelihood for lower returns in a going concern. Also, it can be observed from the Jarque–Bera statistic that all the series are nonnormally distributed. However, we found that most of the returns series are stationary as shown by the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test, except for series such as the aggregated and agricultural commodities. In Table 2, the nonlinearity tests indicate a mixture of linear and nonlinear relationships in the variables at various significance levels. As a result, analysis with the CEEMDANbased RTE is robust for dealing with issues of nonstationarity, nonlinearity, and asymmetric relationships [28].
 
Note. ^{∗}, ^{∗∗}, and ^{∗∗∗} indicate significance at 10%, 5%, and 1% levels, respectively. 
 
Note. ^{∗}, ^{∗∗}, and ^{∗∗∗} indicate significance at 10%, 5%, and 1% levels, respectively. 
3. Results and Discussion
3.1. Reconstruction of IMFs
Analysis of the study is performed using 7 IMFs and a residue decomposed through the CEEMDAN technique for the global commodities and uncertainties. The mean period of each IMF expressed as a ratio of total number of points to the number of peaks, Pearson product moment correlation between each IMF and the original series, the variance of each IMF as a percentage of the original series, and the sum of the entire IMFs and residue are presented in Tables 3 and 4. Specifically, the mean frequency depicts the average frequency of each IMF, and the correlation illustrates the degree of connectedness of each IMF to the original series, whereas the variance of each IMF as a percentage of the original series elucidates the influence of each IMF to the total volatility of the original series [71, 72, 81]. We do these to provide a substantive information about the global commodity and uncertainty dynamics.
 
Note. , , , and denote mean period, Pearson product moment correlations, variance as % of observed, and variance as % of the sum of all IMFs and residue. ^{∗}, ^{∗∗}, and ^{∗∗∗} indicate significance at 10%, 5%, and 1% levels, respectively. 
