key: cord-0687083-x0ojmxuu
authors: Olubusoye, Olusanya E.; Akintande, Olalekan J.; Yaya, OlaOluwa S.; Ogbonna, Ahamuefula E.; Adenikinju, Adeola F.
title: Energy Pricing during the COVID-19 Pandemic: Predictive Information-Based Uncertainty Indexes with Machine Learning Algorithm
date: 2021-09-06
journal: nan
DOI: 10.1016/j.iswa.2021.200050
sha: a8d37f282d388efe8a3b1b04562d08bdb26e01cb
doc_id: 687083
cord_uid: x0ojmxuu

The study investigates the impact of uncertainties on energy pricing during the COVID-19 pandemic using five uncertainty measures that include the COVID-Induced Uncertainty (CIU), Economic Policy Uncertainty (EPU), Global Fear Index (GFI); Volatility Index (VIX), and the Misinformation Index of Uncertainty (MIU). The data, which span between 2-January, 2020 and 19-January, 2021, corresponding to the period of the COVID-19 pandemic. The study finds energy prices to respond significantly to the examined uncertainty measures, with EPU seen to affect the prices of most energy types during the pandemic. We also find predictive potentials inherent in VIX, CIU, and MIU for global energy sources.

The SARS-CoV-2 (also known as Coronavirus of 2019 or COVID-19) disease, detected as viral pneumonia in a restaurant in Wuhan city, China; December 2019, transited from an epidemic to a pandemic following the World Health Organization (WHO) declaration on 11-March, 2020. 1 The pandemic caused global economic uncertainty given the rapid rate of spread and death records in most countries of the world (Hallack & Weiss, 2020) . Its impact on the energy sector was quite severe, especially on the global prices of oil and petroleum products (Olubusoye et al., 2021) . In the early days of COVID-19, when most economic activities were either partially or completely shut down, and various forms of social distancing and isolation measures were put in place, there was a high level of uncertainty that affected both economic production and energy consumption patterns (Hallack & Weiss, 2020) .

The restriction of movement during the peak of the pandemic affected the global energy prices, thus modelling energy price dynamics is primary to improving the economic prospects of global energy and ascertaining the predictive potentials of the uncertainty index proxies for energy prices during the global crisis. Fortunately, this study is not in the vacuum of this procedure. Several studies have researched the impact of COVID-19 on the commodity market, (see for instance; Salisu et al., 2020a, and Olubusoye et al, (2021) among others) and 1 https://www.who.int/news/item/29-06-2020-covidtimeline . Accessed 07/02/2021 other related areas such as misinformation (e.g., Akintande & Olubusoye (2020) , Galvão (2020), among others). Therefore, several extant pieces of literature are detailing different methodological procedures on the subject and COVID-19 related impact on the commodity prices (see Sharif et al., 2020; Salisu & Ogbonna, 2019; Yaya et al., 2017;  among many others).

In the era of Machine Learning 2 (ML) which is characterized by huge datasets handling with great computational speed, we explore the power of an ML algorithm to examine the volatility of energy prices during the pandemic using the COVID induced uncertainty (CIU) and misinformation induced uncertainty (MIU) indexes as well as other uncertainty proxies such as the global volatility index (VIX), economic uncertainty index (EPU) and the global fear index (GFI). This is premised on the study of Herrera et al. (2019) that empirically showed the outperformance of ML over extant econometric models in the generation of accurate forecasts. The choice of energy variables for this study is informed by its wide usage (residential, commercial/industrial, among others) and the role that energy prices play in economic development since energy adoption cuts across different socioeconomic levels.

By using the power of Google, information searches on the web are harnessed via Google trends. Google trends provide relevant subject-based information from web sources such as web searches. The present study, therefore, harnesses this wealth of information reservoir in Google on the COVID-19 pandemic uncertainty, and subsequently adopts Olubusoye et al., (2021) information-based index of uncertainty (the CIU); and also develops a different variant of MIU. The relevance of these Google trends features (the CIU and MIU) are synonymous with deriving market information on the choice of investment to catalyze decisions making on investment, and related ventures. The MIU could promote disobedience of government guidelines towards controlling or limiting the spreads of COVID-19 leading to continuous lockdown or economic inactivity as evident in the case of the US. The CIU and GFI are considered similar to the VIX and the EPU.

This study employs the aforementioned indexes (the CIU, MIU, VIX, EPU, and the GFI) to examine the vulnerability of energy pricing for different energy proxies (Brent oil, diesel, 2 Several studies (see Herrera et al., 2019; Graf et al., 2020) have adopted different Machine Learning algorithms to model and forecast energy commodity prices, as well as energy systems (see Esen et al. (2017) for a detailed review of ML application to heat pump systems.). gasoline, heating oil, kerosene, natural gas, propane, and WTI oil) to COVID-19 pandemic.

In other words, it ascertains whether the adopted and developed uncertainty measures have predictive capabilities for modelling energy prices amidst the COVID-19 pandemic and to what extent they do, as well as the nature of the plausible nexuses between energy prices and uncertainty measures. To achieve this, the study employs the Multivariate Adaptive Regression Spline (MARS) algorithm. This is an ML method that is often used when the relationship of one or more predictor variables to the dependent variable is thought to vary over time. The algorithm accounts for both linear and non-linear relationships of the data features as it provides more predictive power due to its asymmetric structure which induces nonlinearities. Essentially, the adoption of the MARS algorithm is hinged on its characteristic ability to simultaneously account for linearity and non-linearity characteristics of the examined observations, as well as the proven forecast accuracy over econometric models (see Herrera et al., 2019) . While it is robust to the presence of outliers, it also incorporates plausible interactions between variables and accounts for important features of the selected best terms. Our study, to the best of our knowledge, is the first study that considers this approach for energy price modelling.

The rest of the paper is sectioned as follows. Section 2 discusses the global energy uncertainty as it is affected by the pandemic. Section 3 describes the MARS algorithm ML method and its application. Section 4 presents the data analysis and the empirical results.

Section 5 concludes the paper with some policy recommendations.

Our concern in this paper is the Oil-energy of which prices are subject to the economic forces of supply and demand. 3 Before the COVID-19 outbreak, shale oil and gas has had significant effects on the global oil markets. The rising popularity of renewable energy as alternatives to oil-based energy sources is also putting pressure on the global oil market (Akintande et al., 2020 , Olanrewaju et al., 2019 . Thus, the already weakened oil-based energy (oil and gas) was significantly affected by the pandemic and the attendant measures put in place to contain it.

The pricing of each oil-energy source varies depending on fluctuations in the cost of taking the energy source to the market (Plymouth Rock Energy, 2021). During the COVID-19 pandemic, transportation and industrial energy demand declined to almost zero, although, household energy (especially electricity and) demand increased due to stay-at-home advice.

The fall in aggregate energy demand due to movement restrictions and total closure of businesses, international travels, and public & private transportation activities, among many others impacted the environment positively as a result of the reduction in vehicular and industrial emissions of carbon dioxide (CO 2 ) and other poisonous gases. This led to the improvement of air quality in major cities across the world (Chowdhuri et al., 2020; Keremray et al., 2020; Xuelin et al., 2021; and Dang & Trinh, 2021) . While quality air is desirable, economic activities and progress are equally important in many countries, essentially for oil-dependent nations like Nigeria, where the falling oil price imposed significant social and economic costs. There are expectations of global economic recovery in 2021, pushing up oil demand and oil prices. However, the downside risks to the global economic recovery and sustained oil price rally is a resurgence of the pandemic that may result in more lockdowns and less oil demand, low access to vaccines, especially in poorer countries, vaccines hesitancy, and spread of variants of COVID-19. Consequently, some experts suggest that there could be an 8% decline in overall energy demand up to the year 2050, as structural changes, occasioned by COVID-19, impact consumption (Olney, 2021) .

From the supply perspective, oil and gas supplies were also affected as the number of oil and gas rigs reduced drastically, with the US experiencing a drop from 805 rigs to 265 rigs between December 2019 and June 2020 (Statista, 2020) . The pandemic also affected the major supply chain of both oil and gas (IEA 2020); since twenty-two (22) of the twenty-eight (28) global floating production, storage, and offloading vessels under construction in early 2020 were built at shipyards in China, Korea, and Singapore (Nyga-Lukaszewska and Aruga, 2020). However, natural gas prices only dropped mildly, and IEA (2020) reports that the Henry Hub spot price changed from 1.95 USD/million Btu to 1.65 USD/million Btu between 23-January, 2020 and 30-March, 2020.

The collapse of oil prices amid the pandemic and the economic slowdown forced the Organization of Petroleum Exporting Countries (OPEC), 4 and a group of non-OPEC member countries, led by Russia to agree on historic production cuts, as a way to stabilize prices and cause a reversal in the significant drop in the price of oil to a 20-year low (OPEC, 2020).

Between February and March 2020, oil prices hit the lowest price of $10 per barrel in reaction to the COVID-19 pandemic 5 . Energy prices changed quickly in response to news cycles, policy changes, and fluctuations in the world's markets during the pandemic (Bajpai, 2021) . According to Heckman (2017) , markets for electricity, natural gas, oil, and renewable energy are complicated and characterized by uncertainties in the global economy.

Fundamental economic factors such as supply and demand are relatively predictable; however, energy uncertainties, driven by political and regulatory factors, cum financial speculation, make forecasting energy prices more challenging. 6 Other important factors that affect energy pricing include transportation (both commercial and personal), population growth, and seasonal changes (Bajpai, 2021) .

Previous studies on energy have affirmed that energy prices are affected by market forces, gas storage, weather forecasts, generation changes, global markets, imports & exports, government regulation, and financial speculation (Heckman, 2017) . The literature on the determinants of energy prices and fluctuation are considerably numerous, but the novel coronavirus has opened the field up for more debates on energy price uncertainty. The introduction of indexes in monitoring global economic activities could be a tool to understanding the new trend of research on energy prices due to the structural changes caused by COVID-19. Interestingly, there are various indexes for monitoring global uncertainty. We are in an era of unprecedented economic uncertainty, and particularly, with the energy sector.

Performances of the global economy have been influenced by oil price shocks, health crises such as the Spanish flu and COVID-19, war, and political issues, among others this, therefore, necessitated developing global indices of uncertainty. developed the GFI by leveraging the ongoing pandemic. They computed the index as a ratio of the number of confirmed COVID-19 cases and the number of recorded deaths. Olubusoye, et al. (2021) developed the CIU index and applied it to examine the vulnerability of energy prices during the pandemic period. In comparison with EPU, GFI, and VIX index, their results showed that energy prices lack hedging potentials against the uncertainty occasioned by the COVID-19 pandemic and the sensitivity of CIU to energy prices. 5 In fact, at some point the price of WTI crude oil went into negative territory. 6 The previous similar case of a global pandemic was the Spanish Flu of 1918.

The importance of energy prices and the decline in demands due to pandemic-associated uncertainties serves as a motivation to investigate how uncertainty indexes impact energy prices. This study develops similar indexes to Salisu & Akanni (2020) but differs in the computational method and the variables under consideration. Many existing indexes (leveraged on the COVID-19) are computed based on reported infection and mortality figures. These indexes are limited. Since access to quality information (Akintande & Olubusoye, 2020) is most likely to affect an individual's perception and decision more than the infection and mortality figures. Thus, misinformation may catalyze the understanding of investment risks (Norouzi et al., 2020) . Consequently, the yearnings for quality information about the pandemic forms an essential level of uncertainty.

Multivariate Adaptive Regression Spline (MARS) is a form of the regression model (Friedman, 1991) 

Given X and Y; independent and dependent variables, respectively; MARS relies on a hypothesis of the form:

where is the basis function weighted sum, and 's are constant coefficients. The basis function has one of the following forms; (1) a constant, (2) a hinge function, (3) and a product of two or more hinge functions. The hinge function has the form; Essentially, if we say we have Y = f(X), then the hinge function is h(X-a), where -a‖ is the cut-off point value; and for a single knot, the hinge function will result in two linear models for Y, that is,

Once the first knot has been obtained, the search continues for a second knot that is obtained at X = a 2 . This results in three linear models for Y as in (4). This process continues until a potential and highly non-linear prediction equation is achieved. While obtaining several knots is possible, the MARS algorithm introduces pruning, to find the optimal number of knots and removes the insignificant knots to arrive at the best predictive accuracy.

MARS builds a model in two phases namely; the forward and the backward pass. These two stages bear some semblances in recursive partitioning trees (Friedman, 1991) . The forward MARS model starts with the intercept term (i.e., the mean of the response values). It then repeatedly sums the basic functions in pairs to the model. In each step, it computes the pair of basic functions ( ), which provides the maximum reduction in the sum of squares residual error (sort of greedy algorithmsee Black (2005)). The two basic functions are expected to be identical except that each is on a different part of the mirrored hinge function. Thus, a hinge function is defined by a variable and a knot. MARS searches parent terms, all variables (to pick one for the new, ), and all values of each variable (for the knot of the new hinge function) to compute the coefficient of each term by applying a linear regression over the parents. This term's summation iterates until the change in residual error are reduced. In other words, the process terminates when the maximum number of terms (parents) is reached. Note that the maximum possible terms are usually specified by the users before the MARS iteration starts. This task is faster if a more rational procedure is adopted (Friedman, 1993) . The backward process proposes to solve the over-fitting problem of the forward process.

Hence, the backward process prunes the hypothesis. It removes the terms one after the other, by deleting the least efficient term at each step until it reaches the best sub-hypothesis. The hypothesis subsets are assessed with the generalized cross-validation (GCV) criterion (Craven & Wahba, 1978) . Thus, the algorithm for the GCV is given as:

where E -efficient number of parameters, and Mnumber of observations. and ( ) , where number of MARS terms, and Ppenalty. The ( ) is the number of hinge-function knots. Note that for the penalty, about 2 or 3 is allowable.

The data employed in this study are daily energy ( from and CIU (based on Google trends search volume) from the procedure described in Olubusoye et al. (2021) . It is informed by the perceived connectedness and possible bidirectional causality of uncertainty and misinformation, as the latter is likely to spur the former, while the uncertainty could breed an opportunity for misinformation (see Akintande & Olubusoye, 2020) . Hence, we consider search volumes on the Google Trends database relating to misinformation around the COVID-19 pandemic, using keywords such as "COVID-19 Fake news", "Fake news", "COVID-19 Myth", "COVID and Age", "COVID and Race" and "COVID and Bleach". Following Olubusoye et al. (2021) and Salisu et al. (2021) , we generate a single factor from the principal component analysis of these search volumes. This factor is re-scaled to range between -a‖ and -b‖, using

such that a = 0 and b = 100 correspond extreme cases of no misinformation and the highest level of misinformation, respectively.

Between January 2, 2020, and January 19, 2021, the price of Brent fluctuates between 9.12 and 70.25 USD per barrel. The price resonates around 50.88 USD and is valued averagely While (during the study period), the upward trends are evident, and no energy (sources) price has rebound to its initial high as when writing this paper. The crux of this study is to obtain a predictive accuracy of the impact of the uncertainties on various energy prices. We present the predictive hypothesis of the MARS algorithm in Section 3.2. We modelled the algorithm using the K-fold CV scheme, and the best folds are reported based on the RMSE and MAE values. Most importantly, the 10-folds CV is more favorable except for NGAS and Propane, where we adopt the 5-folds CV for the best predictive model. Similarly, this approach facilitated picking the most appropriate prune and degree for the final predictive hypotheses by setting the degree between 1 and 3 and the prune between 2 and 100. Essentially, the best MARS algorithm pruning and degree (to find the optimal number of knots) follows standard algorithmic procedures. And free from authors' bias and influence.

Diesel & Gasoline Heating

On the resulting figures on the tables (Tables 2 -9) , we obtain the impact of a given uncertainty measure on the considered energy price by taking the product of the knot/hinges (main and interactions) value and the estimated coefficients. It is noteworthy to state that the positively (negatively) signed coefficients will imply that a corresponding uncertainty measure would increase (decrease) in the energy price. We highlighted the model adequacy (GRSq., RSq., RMSE and MAE); and the order of importance for each uncertainty measure. The best predictive algorithm for NGAS price is degree 1 (Brent and WTI are of degree 2). It implies that the effect of the features is insignificant. Thus, CIU has a shock of 62.45, which leads to a 4.1037 USD decline in NGAS and 4.2775USD in NGAS recovery price. The MIU effect leads to 0.3379USD in NGAS recovery. Similarly, the EPU effect leads to a 0.399USD decrease in NGAS price and 0.6806USD NGAS recovery price. The effect of VIX leads to a 1.0734 USD decline in NGAS price and a 0.7708USD increase or price recovery of NGAS. The GFI has no significant direct influence on NGAS price. The effects of all the uncertainty proxies except MIU are bidirectional (see Table 4 ).

Diesel price is most affected by VIX, EPU, and MIU, respectively. The EPU index has the most significant ( Table 5 . Table 6 ). Table 7 ). respectively (see Table 8 ). have unidirectional and inverse effects on propane prices. On the other hand, the impact of the uncertainty proxies has direct relationships with propane prices. In short, CIU, EPU, GFI, and VIX directly and individually cause 0.3348USD, 0.0892USD, 0.2870USD, and 0.1359USD decline in the propane price. 

The study investigates the effect of uncertainty on energy prices using eight energy prices -Brent oil, Diesel, Gasoline, Heating Oil, Kerosene, Natural Gas, Propane, and WTI oil; and

with five different uncertainty measures -COVID Induced Uncertainty (CIU), Economic

Policy Uncertainty (EPU), Global Fear Index (GFI), Volatility Index (VIX), and Misinformation Index of Uncertainty (MIU). Given that misinformation spread during the pandemic, we develop the MIU. We formulated the hypothesis using all the uncertainty proxies as input and the energy prices as output. The descriptive statistics of the energy prices reveals that the trend throughout the study is bidirectional. Imperatively, each energy price has unique characteristics of downward (price decline) and upward (price recovery) movement. Essentially, the hypotheses on the energy prices reveal that uncertainty affects energy prices in both ways.

More formally, we examined the nexus between the energy prices and uncertainty proxies under the ML algorithm. In addition, it reveals the impact of each uncertainty proxy and indicates an ordering of their importance in the predictive model for energy prices. While we find most of the uncertainty measures to have the predictive potential for the energy prices, this is not true for GFI. It may not be unconnected with its health inclination that limits its predictive potential for energy prices. Hence, it should be employed when dealing with health-related phenomena. The order of inherent predictive power in the included uncertainty proxies appears to be sensitive to the energy price under study. As observed, the EPU influences the predictive fluctuations in most of the energy price uncertainty during the pandemic. The VIX, CIU, MIU, and GFI follow the EPU in that order. The contributing influence of the EPU is not surprising because many policies are proffer quickly to arrest the spread of the disease, which may have heightened the uncertainty around economic activities -a characteristic feature that informed the development of the EPU. The other uncertainty proxies are not specific to the energy sector as much as the EPU. Hence their observed position in the ordering of their relevance. Generally, energy prices' responses to economic uncertainties are mostly bi-directional.

In contrast to the findings of Olubusoye et al. (2021) and that assume linear nexus between energy prices and economic uncertainty measures; and respectively found negative and positive responses of energy commodity prices to uncertainty measures, ML further beams the light on the non-linear nature of the nexus, as well as the existence of time-varying parameter. Hence, the plausibility of both positive and negative responses that depict a bullish and bearish period in the energy price series. Therefore, given the reaction of energy prices on uncertainty and (more prominently) economic policy uncertainty, our findings bear some implications for policymakers. Policies that affect economic productivity are most likely to affect energy pricing since most products are; either energy-dependent or energy-related. Hence, while attempting to curtail a crisis (epidemic or pandemic), the economic activities should inescapably remain active but not be halted. Efforts such as a virtual working environment and adoption should (from now) remain a viable option.

Akintande, O.J., and Olubusoye, O.E. (2020) . Datasets on how misinformation promotes Immune perception of COVID-19 pandemic in Africa. Data in Brief, 31, 106031.

76USD increase in WTI price, and MIU accounts for a 5.955USD increase in WTI price. Also, EPU accounts for 23.149USD, and VIX accounts for a 46.140USD increase in the price of WTI. The decline and recovery plot

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I write to submit our manuscript for publication in your high impact journal. The study investigates the effect of uncertainty on energy prices; using eight energy prices -Brent oil, Diesel, Gasoline, Heating Oil, Kerosene, Natural Gas, Propane, and WTI oil; and five different uncertainty measures -COVID Induced Uncertainty (CIU), Economic Policy Uncertainty (EPU), Global Fear Index (GFI), Volatility Index (VIX), and Misinformation Index of Uncertainty (MIU). The last uncertainty index was developed in this study, given that the pandemic was also characterized by several misconceptions about the disease.We formulated the hypothesis using all the uncertainty proxies as input on each of the energy prices as output. The descriptive statistics of the energy prices reveals that the trend throughout the study is bidirectional. Imperatively, each energy price has unique characteristics of downward (price decline) and upward (price recovery) trends. Essentially, the hypotheses on the energy prices reveal that uncertainty affects energy prices in both ways. We adopt the MARS algorithm to investigate the feature contributions.

I writes to confirm that both authors of this work agreed to publish this work in your journal and both authors have no conflict of interest.

Many thanks for giving us the opportunity of resubmitting the above paper in Intelligent Systems with Applications journal.We have made corrections proposed by the anonymous reviewer and as suggested by the Main Editor, and we hope the paper might be given favourable judgement.