<big>'''Influencing Factors on Natural Gas Price Volatility with Special Attentions on Immediate Impacts of Covid-19: Multiple Linear Regression Analysis'''</big>

<big>Ljubiša Stajić^a, Bojan Đorđević^b, Silvana Ilić^b and Dejan Brkić^ac*</big>

'''Abstract:''' The paper examines the primary drivers and factors influencing the volatility of natural gas prices in the world from January 2007 to July 2020. In addition to the narrow dependence and spillover of crude oil and natural gas prices, the impact of demand shocks as well as structural shocks when it comes to supply or global supply in the natural gas market and the impact of renewable energy production and coal production at the price of natural gas has been shown, with special reference to the outbreak of the COVID-19 pandemic. For that purpose, the method of multiple linear regression was used. The results show that the sensitivity of natural gas prices significantly depends on the regime and type of the shock in the natural gas market, and that the total production of energy from renewable sources, production of coal and natural gas and the price of crude oil have a significant impact on the price of gas.

'''Keywords''': Energy Prices; Natural Gas; Multiple Linear Regressions; Renewable Energy; Price Volatility; Energy Consumption; COVID-19

Natural gas is a mixture of hydrocarbons and methane and due to the fact that it mixes easily with air and has a high combustion rate without smoke, soot and solid residues, it has a significant environmental advantage over conventional fuels such as oil and coal. In the same way that oil replaced coal in industrial production at the beginning of the twentieth century, gas suppressed oil at the beginning of the twenty-first century and became an increasingly common fuel used to start the industry. Due to the fact that natural gas is a much cleaner energy source, this tendency in many developed countries is regulated by law, so some industrial sectors are forced to start their production with the help of natural gas. Given the world’s growing concern about the effects of carbon dioxide emissions from fossil fuels, and the impact on climate change and low carbon content in natural gas compared to other fossil fuels, natural gas has become a major energy source in many economies across the globe. Recent research shows that the consumption of natural gas plays an important role in facilitating economic growth in both short and long term [1] and that disruptions in the supply of natural gas entails huge economic costs [2,3]. Fluctuations in energy prices are also becoming increasingly important in influencing risk reduction and strategic investments [4,5].

The largest recorded shock demand in the history of global natural gas markets happened in the first half of 2020. Faced with historically mild temperatures during the first months of the year, the COVID-19 pandemic hit the already declining demand for gas. Gas consumption is expected to fall by 4% in 2020, due to successive lower demand for warm winter heating, the implementation of lockdown measures in almost all countries and territories, to slow the spread of the virus and lower activity generated by the macroeconomic crisis caused by the pandemic. Faced with this unprecedented shock, natural gas markets are undergoing strong supply and demand adjustments, resulting in historically low spot prices and high volatility. Demand for natural gas is expected to gradually recover in 2021, but the COVID-19 crisis will have a longer-term impact on natural gas markets, as major medium-term drivers are subject to great uncertainty [6,7].

With the above mentioned, the contribution of our work to literature is that by using multiple linear regression (MLR) [8,9] we prove that selected independent variables are important and necessary in determining the dependent variable and that there is a significant relationship and interaction between selected factors and natural gas prices. We also prove that fluctuations in natural gas prices are correlated with certain global economic events. We show how the two most significant depressions in recent history - the global economic crisis and COVID-19, have affected the price of natural gas, which can be useful in further research, forecasting prices and consumption in the energy markets, especially when it comes to increased risk of potentially new infectious diseases in the global market in the near future.

The rest of the work is organized as follows: Section 1 – Introduction; Section 2 - Data on energy consumption and natural gas reserves; Section 3 - Movement of natural gas prices in the selected period; Section 4 - Literature overview; Section 5 - Selected data; Section 6 - Methodology used in the research; Section 7 - Results with discussion, and Section 8 - Conclusions. Finally, in section 8, we provide a list of literature that was used during the preparation of this paper.

==2. Energy Consumption and Natural Gas Reserves in the World==

The development of society is significantly conditioned by the increase in energy consumption. Primary energy consumption is constantly growing. During the period from 1870 until 1970 year, energy consumption in the world increased 32 times with an average growth rate of 3.5%. Only in the course of the last twenty years (1950-1970) of the period in question, the energy consumption was higher than the total consumption from the year 1850 until the year of 1950. In the period from 1973 to 2019, energy consumption more than doubled (Table 1). The total energy consumption of the world in 2019, was 14,858 Mtoe. Primary energy consumption is not uniform in the world, nor proportional to the population size of various regions. Developed countries consume over 50% of the world's total energy today, and at the same time, their citizens amount to approximately 20% of the total population.

'''Table 1.''' The world’s energy consumption by fuel type

{| style="width: 87%;border-collapse: collapse;"

|  rowspan='3' style="border-top: 1pt solid black;"|No.

|  rowspan='3' style="border-top: 1pt solid black;"|Type of fuel

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|1960

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|3.345 Mtoe

| Natural gas

| 21.6

The most significant change, in percentage, in the structure of the total energy consumption, by type of fuel in the period 1960-2019 has natural gas as a fuel, which has increased its share from 12% to 21.6%. Oil as a fuel recorded a decline in its share in the structure of total energy consumption of the world from 45% in 1973 to 31.7% in 2019. Gas as an energy source in the period of four and a half decades (1973-2019) increased from 16% to 21.6%. This increase in the gas consumption shows its increasingly pronounced and significant role in the energy market today. Based on the current trend of the past sixty years, but also all available data and indicators, the prevailing expert opinion is that its role and position in the coming decades will be even more pronounced and dominant in the energy market (EIA - Energy Information Administration).

Figure 1 shows 15 countries that are the largest consumers of natural gas in the world.

[[Image:Review_988885787501-image1.png|450px]]

'''Figure 1.''' The largest consumers of natural gas in 2019 (in billion m³), Source: EIA Beta ([https://www.eia.gov/beta/international/ https://www.eia.gov/beta/international/])

When it comes to the world’s reserves and resources, two terms are not interchangeable, first meaning the amount that can be processed, and second the entire amount of material that exists in a country. Estimates of the world’s reserves of energy of fossil origin are different. There are over 700 oil and gas basins in the world, and about 400 have been explored so far, of which 160 are being exploited. The reserves of these energy sources are extremely unevenly distributed within the basins as well. Natural gas occupies a significant place of the world's energy resources. Observed from the aspect of current possibility of exploitation and production of natural gas, at the existing level of technical-technological development and economic profitability, all gas deposits in nature can be grouped into conventional and unconventional. Conventional gas deposits are those deposits from which, at present moment, gas can be exploited in an economically viable manner with a constant supply of fuel.

Figure 2 shows the 15 largest natural gas producers in the world in 2019.

[[Image:Review_988885787501-image2.png|444px]]

'''Figure 2.''' The largest producers of natural gas in 2019 (in billion m³), Source: EIA Beta ([https://www.eia.gov/beta/international/ https://www.eia.gov/beta/international/])

 

About 80% of the world's conventional gas reserves are located in only 10 basins. Estimates of total gas reserves in the world tend to increase steadily. In 1995, total conventional reserves were estimated at 142.36 x 10¹² m³. Five years later, total reserves were approximated at 158.46 x 1012 m³. In 2005, they were estimated to be 175.66 x 10¹² m³, while it was believed that the total gas reserves were 192.46 x 10¹² m³ in 2010 worldwide. While it was roughly calculated that the total conventional gas reserves are two hundred and two trillion m³ back in 2019.

 

 

[[Image:Review_988885787501-image3.png|456px]]

 

'''Figure 3.''' Countries with the largest estimated natural gas reserves in 2019 (in trillions of m³), Source: EIA Beta ([https://www.eia.gov/beta/international/ https://www.eia.gov/beta/international/])

 

 

==3. Natural Gas Prices==

 

 

 

However, natural gas prices fell sharply since the beginning of 2020 due to weak demand and abundant supply. European natural gas prices fell to a decade-long low and have fallen by almost 40% since early 2020. U.S. natural gas prices have fallen slightly, in part because they had already been low. Price differences between regional benchmarks for natural gas continued to decline, mostly driven by increasing availability of liquefied natural gas. However, the fall in prices of natural gas and coal is smaller than the price of crude oil, which has fallen by about 65% since January 2020. Natural gas and coal are primarily used for electricity generation and industrial purposes, not for transportation. As such, lockdowns and travel restrictions had less of an impact on demand for these products than for crude oil.

 

 

Natural gas prices are expected to recover from the current lows, but will still be about 25% lower than in 2019. Demand for natural gas is expected to gradually recover from current low levels after lifting the lockdown, but will remain below 2019 levels. Demand for coal is likely to remain weaker, as a part of the ongoing transition from coal to natural gas in global electricity generation. ([http://www.worldbank.org www.worldbank.org]: [https://blogs.worldbank.org/opendata/will-natural-gas-and-coal-prices-recover-coronavirus-covid-19-slump https://blogs.worldbank.org/opendata/will-natural-gas-and-coal-prices-recover-coronavirus-covid-19-slump]).

 

Global gas demand could fall by 4% annually in 2020. This would be the largest drop in gas demand ever recorded since the development of the gas industry in the second half of the 20th century. By comparison, gas demand fell by 2% in 2009 due to the global financial crisis. About 75% of demand loss is likely to occur in developed gas markets across Europe, North America, the Commonwealth of Independent States (CIS), and Asia due to lower electricity demand, declining industrial activity, and lower space heating needs in the commercial sector [7].

 

 

 

| [[Image:Review_988885787501-image4.png|258px]]

| [[Image:Review_988885787501-image5.png|center|264px]]

<span id='_Hlk69042703'></span>'''Figure 4.''' Fluctuation of production and consumption of natural gas from January 2007 - September 2020 (general trends). Source: U.S. Energy Information Administration - Monthly Energy Review

 

 

{|

| [[Image:Review_988885787501-image6.png|258px]]

| [[Image:Review_988885787501-image7.png|center|252px]]

'''Figure 5.''' Fluctuation of production of coal and energy from renewable sources from January 2007 - September 2020 (general trends). Source: U.S. Energy Information Administration - Monthly Energy Review

 

 

{|

| [[Image:Review_988885787501-image8.png|246px]]

| [[Image:Review_988885787501-image9.png|center|270px]]

'''Figure 6'''. Fluctuation of prices of crude oil and natural gas from January 2007 - September 2020 (general trends), Source: FRED Graph Observations, and Henry Hub Natural Gas Spot Price, respectively

==4. Literature Review==

Much of the literature on the natural gas market is devoted to examining the relationship between natural gas prices and the crude oil market, suggesting that oil price fluctuations are important determinants of natural gas prices [10-23]. Only a few studies examined the role of supply and demand factors in determining prices in the U.S. natural gas market. Some recent studies show that, unlike globally defined crude oil markets, natural gas markets are regionally segmented, suggesting that natural gas prices are formed by regional supply-demand relationships [24-27]. Following the recent decoupling of the relationship between the crude oil and natural gas markets [17], it is crucial to understand how natural gas prices respond to supply and demand in times of natural gas market shocks, and to identify the relative contribution factors of each. Accordingly, authors Nick and Thoenes [28] use a structural VAR model to examine price volatility in the German natural gas market. They conclude that supply shocks have a significant impact on the German natural gas market, and that temperature, storage and supply shocks lead to relatively short-term effects, while oil and coal price shocks result in more lasting effects on gas prices.

The relationship between the prices of natural gas and coal was also investigated by Everts et al. [29]. The study used a basic market price replication model with an analysis of the impact of changes on the individual price drivers such as coal prices or subsidies for renewable energy production. The study showed the fall in electricity prices in Germany in the period 2008-2014 can be attributed to market effects such as a reduction in coal use and gas prices as well as a reduction in electricity demand (50%). Only approximately 30% of price reductions could be directly related to subsidies for energy from renewable sources such as wind and solar energy. Authors Mosquera-López and Nursimulu [30] came to qualitatively similar conclusions. They found that in the short and medium term, the main drivers of prices differ and vary in time. In the case of the spot market, determinants of prices were renewable sources and demand for electricity, while in the future markets the main drivers of natural gas prices were the supply and price of coal.

Mu [31] identifies a demand for natural gas in relation to weather conditions as an important factor influencing the movement of gas prices. Hulshof et al. [32] conclude that natural gas prices are mainly determined by the weather conditions and availability of stored quantities, while supply has no significant effect. The availability of natural gas in storage and the outside temperature negatively affected the price of natural gas. They also concluded that the price of natural gas was related to the production of electricity from wind.

 

 

 

 

 

 

{| class="formulaSCP" style="width: 100%; text-align: center;"  

{| style="text-align: center; margin:auto;"  

| <math display="inline">{Y}_{i\, }=\, {\beta }_{0\, }+\, {\beta }_{1}{x}_{1i\, }+\, \cdots \, +</math><math>\, {\beta }_{k}{x}_{ki}\, +\, {\epsilon }_{i}</math>

| style="width: 5px;text-align: right;white-space: nowrap;" | (1)

 

where Y is the dependent variable, β₀ – regression constant, x₁, x₂ … x_k – independent variables, ε - standard error i.e. residues, β - unknown parameter to be evaluated (regression parameter).

Sample estimates of unknown parameters are obtained by applying the method of least squares. In the case of models with two independent variables, the following function needs to be minimized, Eq. (2):

{| class="formulaSCP" style="width: 100%; text-align: center;"  

{| style="text-align: center; margin:auto;"  

| <math display="inline">F\left( \hat{{b}_{0},}\hat{{b}_{1}},...,\hat{{b}_{k}}\right) =</math><math>\sum _{i=1}^{n}{\epsilon }_{i}^{2}=\sum _{i=1}^{n}{\left( {y}_{i}-\hat{{y}_{i}}\right) }^{2}=\sum _{i=1}^{n}{\left( \hat{{b}_{0}}+\hat{{b}_{1}}\cdot {x}_{1i}+\hat{{b}_{k}}\cdot {x}_{2i}\right) }^{2}</math>

| style="width: 5px;text-align: right;white-space: nowrap;" | (2)

Minimization of the function F is achieved by equalizing its partial derivatives of the first order by parameters, with zero, Eq. (3):

{| class="formulaSCP" style="width: 100%; text-align: center;"  

{| style="text-align: center; margin:auto;"  

| <math display="inline">\begin{matrix}\frac{\partial F}{\partial \hat{{b}_{0}}}=0\\\frac{\partial F}{\partial \hat{{b}_{1}}}=0\\\begin{matrix}\vdots \\\frac{\partial F}{\partial \hat{{b}_{k}}}=0\end{matrix}\end{matrix}</math>

| style="width: 5px;text-align: right;white-space: nowrap;" | (3)

 

{| class="formulaSCP" style="width: 100%; text-align: center;"  

{| style="text-align: center; margin:auto;"  

| <math display="inline">\sum _{i=1}^{n}{Y}_{i}=n\cdot \hat{{b}_{0}}+\hat{{b}_{1}}\cdot \sum _{i=1}^{n}{x}_{1i}+\ldots +\hat{{b}_{k}}\cdot \sum _{i=1}^{n}{x}_{ki}</math>

| style="width: 5px;text-align: right;white-space: nowrap;" | (4)

{| class="formulaSCP" style="width: 100%; text-align: center;"  

{| style="text-align: center; margin:auto;"  

| <math display="inline">\sum _{i=1}^{n}{{x}_{1i}\cdot Y}_{i}=\hat{{b}_{0}}\cdot \sum _{i=1}^{n}{x}_{1i}+\hat{{b}_{1}}\cdot \sum _{i=1}^{n}{x}_{1i}^{2}\ldots +\hat{{b}_{k}}\cdot \sum _{i=1}^{n}{{x}_{1i}\cdot x}_{ki}</math>

| style="width: 5px;text-align: right;white-space: nowrap;" | (5)

whose solution yields sample grades b₀, b₁,…,b_k, of unknown parameters β₀,…,β_k.

 

{| class="formulaSCP" style="width: 100%; text-align: center;"  

{| style="text-align: center; margin:auto;"  

| <math display="inline">X'Y=\left( X'X\right) \hat{b}</math>

| style="width: 5px;text-align: right;white-space: nowrap;" | (6)

Wherein X ' transposed matrix of matrix X, follows, Eq. (7abc):

 

<math display="inline">{X}^{'}Y=\left[ \begin{matrix}\sum _{i=1}^{n}{Y}_{i}\\\sum _{i=1}^{n}{x}_{1i}\cdot {Y}_{i}\\\begin{matrix}\vdots \\\sum _{i=1}^{n}{x}_{ki}\cdot {Y}_{i}\end{matrix}\end{matrix}\right]</math>  (7a)

 

<math display="inline">{X}^{'}X=\left[ \begin{matrix}n&\sum _{i=1}^{n}{x}_{1i}&\begin{matrix}\ldots &\sum _{i=1}^{n}{x}_{ki}\end{matrix}\\\sum _{i=1}^{n}{x}_{1i}&\sum _{i=1}^{n}{x}_{1i}^{2}&\begin{matrix}\ldots &\sum _{i=1}^{n}{x}_{1i}\cdot {x}_{ki}\end{matrix}\\\begin{matrix}\vdots \\\sum _{i=1}^{n}{x}_{ki}\end{matrix}&\begin{matrix}\vdots \\\sum _{i=1}^{n}{x}_{1i}\cdot {x}_{ki}\end{matrix}&\begin{matrix}\begin{matrix}\ddots \\\ldots \end{matrix}&\begin{matrix}\vdots \\\sum _{i=1}^{n}{x}_{ki}^{2}\end{matrix}\end{matrix}\end{matrix}\right]</math>  (7b)

 

<math display="inline">\hat{b}=\left[ \begin{matrix}\hat{{b}_{0}}\\\hat{{b}_{1}}\\\begin{matrix}\vdots \\\hat{{b}_{k}}\end{matrix}\end{matrix}\right]</math>  (7c)

By solving the matrix equation, a solution for the evaluation vector is obtained <math display="inline">\hat{b}</math>, Eq. (8):

{| class="formulaSCP" style="width: 100%; text-align: center;"  

{| style="text-align: center; margin:auto;"  

| <math display="inline">\hat{b}={\left( X'X\right) }^{-1}\left( X'Y\right)</math>

| style="width: 5px;text-align: right;white-space: nowrap;" | (8)

 

{| class="formulaSCP" style="width: 100%; text-align: center;"  

{| style="text-align: center; margin:auto;"  

| <math display="inline">\hat{b}:N\left( \beta ;{\sigma }^{2}{\left( X'X\right) }^{-1}\right)</math>

| style="width: 5px;text-align: right;white-space: nowrap;" | (9)

 

{| class="formulaSCP" style="width: 100%; text-align: center;"  

{| style="text-align: center; margin:auto;"  

| <math display="inline">T=\frac{\hat{{b}_{j}}}{\sqrt{\frac{{a}_{ii}\cdot \sum _{i=1}^{n}{\epsilon }_{i}^{2}}{n-k-1}}}</math>

| style="width: 5px;text-align: right;white-space: nowrap;" | (10)

This random variable, in the case of the correct hypothesis H₀: βj, has a T distribution with n – k – 1 degrees of freedom, where the k is number of independent variables, аnd a_ii is i-th diagonal element of the matrix (X’X)^-1.

<span id='_Hlk67674194'></span>The basic assumption in the formation of a multilinear regression model is the normal distribution of residual variable models. Table 2. shows the minimum and the maximum values of all variables and their standard deviations (Standard Deviation) between the minimum and the maximum values in the observed period.

'''Table 2.''' Original variables with parameters from descriptive statistics.

 

{| style="width: 80%;border-collapse: collapse;"

|-

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Variable

| style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Minimum

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Maximum

| style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Mean

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Std. deviation

|  style="border-top: 1pt solid black;vertical-align: bottom;"|Natural Gas Price

|  style="border-top: 1pt solid black;vertical-align: bottom;"|1.63

|  style="border-top: 1pt solid black;vertical-align: bottom;"|12.69

|  style="border-top: 1pt solid black;vertical-align: bottom;"|3.95

|  style="border-top: 1pt solid black;vertical-align: bottom;"|1.96

|-

|  style="vertical-align: bottom;"|Crude Oil Price

|  style="vertical-align: bottom;"|16.55

|  style="vertical-align: bottom;"|133.88

|  style="vertical-align: bottom;"|71.73

|  style="vertical-align: bottom;"|23.73

|-

|  style="vertical-align: bottom;"|Natural Gas Production

|  style="vertical-align: bottom;"|1878.00

|  style="vertical-align: bottom;"|3.620.71

|  style="vertical-align: bottom;"|2.603,39

|  style="vertical-align: bottom;"|426.78

|-

|  style="vertical-align: bottom;"|Natural Gas Consumption

|  style="vertical-align: bottom;"|1460.04

|  style="vertical-align: bottom;"|3.417.20

|  style="vertical-align: bottom;"|2192.16

|  style="vertical-align: bottom;"|450.96

|-

|  style="vertical-align: bottom;"|Renew. Eng. Source Prod.

|  style="vertical-align: bottom;"|483.32

|  style="vertical-align: bottom;"|1063.77

|  style="vertical-align: bottom;"|789.28

|  style="vertical-align: bottom;"|142.78

|-

|  style="border-bottom: 1pt solid black;vertical-align: bottom;"|Coal Production

|  style="border-bottom: 1pt solid black;vertical-align: bottom;"|36934.07

|  style="border-bottom: 1pt solid black;vertical-align: bottom;"|104389.50

|  style="border-bottom: 1pt solid black;vertical-align: bottom;"|77.800.98

|  style="border-bottom: 1pt solid black;vertical-align: bottom;"|15804.46

We will use software to build regression models SPSS and XLSTAT.

In order to assess the quality of the acquired regression models, i.e. to assess the reliability and the impartiality, we need to perform several econometric tests. The first test is to examine the absence of multicollinearity. This test uses two determinants: Variance Inflation Factor (VIF) and Tolerance Factor (TOL). If the tolerance value is less than 0.2 or 0.1 and at the same time the VIF value is 10 or more, then multicollinearity is problematic. The problem of multicollinearity does not exist when the values of VIF are <5 and 10, respectively, while the values of TOL are <0.2 and 0.1, respectively. Variables whose VIF values are greater than 10 and TOL> 0.4 indicate a multicollinearity problem and should not be in the model. The second test refers to the normal distribution of variables in the model, which will be tested using Shapiro-Wilk and values of two coefficients: asymmetry (skewness) and flatness (kurtosis) for which acceptable values of variables are approximately ± 1. The third assumption of the standard model refers to the control of the random error of homoskedasticity or heteroskedasticity. It is necessary that random errors show the same level of distribution around their mean value. When random variances of errors differ significantly from each other, it is a case of heteroskedasticity. This testing will be performed by Breusch-Pagan (based on testing the dependence of residual variation on the height of all regressors) and White's test (based on comparing the variance of estimators obtained by the method of least squares under conditions of homoskedasticity and heteroskedasticity). Autocorrelation of residues is a common occurrence in the case of economic time series, which is the fourth test or assumption of the standard model. We will apply the Durbin-Watson test to detect autocorrelation. Values of this test can range from 0 to 4. Values greater than 2 indicate negative, while values less than 2 indicate positive autocorrelation.

<span id='_Hlk67674533'></span>

==7. Results and Comments==

<span id='_Hlk67674344'></span>Results of the Pearson correlation coefficient show a relatively strong statistical relationship between the price of natural gas and the price of crude oil, natural gas production, renewable energy production and coal production, except for gas consumption where the natural gas price relationship is weak. The highest level of positive correlation with the dependent variable is achieved by coal production (0.654), followed by the price of crude oil (0.527), while the gas production (-0.629) and energy production from renewable sources (-0.663) variables are highly correlated, but with the opposite sign. The correlation matrix is given in Table 3.

'''Table 3.''' Pearson correlation matrix.

{| style="width: 67%;border-collapse: collapse;"  

|-

| style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Variable

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|(1)

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|(2)

| style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|(3)

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|(4)

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|(5)

| style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|(6)

|  style="border-top: 1pt solid black;vertical-align: bottom;"|(1)

|  style="border-top: 1pt solid black;vertical-align: top;"|1.000

|  style="border-top: 1pt solid black;vertical-align: top;"|'''0.527'''

|  style="border-top: 1pt solid black;vertical-align: top;"|'''-0.629'''

|  style="border-top: 1pt solid black;vertical-align: top;"|-0.264

|  style="border-top: 1pt solid black;vertical-align: top;"|'''-0.663'''

|  style="border-top: 1pt solid black;vertical-align: top;"|'''0.654'''

|-

|  style="vertical-align: bottom;"|(2)

|-

|  style="vertical-align: bottom;"|(3)

|-

|  style="vertical-align: bottom;"|(4)

|-

|  style="vertical-align: bottom;"|(5)

|-

|  style="border-bottom: 1pt solid black;vertical-align: bottom;"|(6)

|  style="border-bottom: 1pt solid black;vertical-align: top;"|0.654

|  style="border-bottom: 1pt solid black;vertical-align: top;"|0.635

|  style="border-bottom: 1pt solid black;vertical-align: top;"|-0.848

|  style="border-bottom: 1pt solid black;vertical-align: top;"|-0.447

|  style="border-bottom: 1pt solid black;vertical-align: top;"|-0.843

|  style="border-bottom: 1pt solid black;vertical-align: top;"|1.000

Table 4. shows the Skewness and Kurtosis coefficients. Results for all variables are within the acceptable value of ± 1. The value of the Shapiro -Wilk test is also within the acceptable limit values, so we can conclude that a normal distribution of variables in the model has been achieved.

'''Table 4.''' Checking the normality of the distribution of dependent variables in the model.

{| style="width: 80%;border-collapse: collapse;"  

| rowspan='2' style="border-top: 1pt solid black;"|Variables

|  style="border-bottom: 1pt solid black;vertical-align: bottom;"|Statistic

|  style="border-bottom: 1pt solid black;vertical-align: bottom;"|Std. Error

| style="border-bottom: 1pt solid black;vertical-align: bottom;"|Statistic

|  style="border-bottom: 1pt solid black;vertical-align: bottom;"|Std. Error

|  style="border-top: 1pt solid black;vertical-align: top;"|Crude Oil Price

|  style="border-top: 1pt solid black;vertical-align: top;"|0.208

|  style="border-top: 1pt solid black;vertical-align: top;"|0.190

|  style="border-top: 1pt solid black;vertical-align: top;"|-0.739

|  style="border-top: 1pt solid black;vertical-align: top;"|0.377

|-

|  style="vertical-align: top;"|Natural Gas Production

|  style="vertical-align: top;"|0.655

|  style="vertical-align: top;"|0.190

|  style="vertical-align: top;"|-0.394

|  style="vertical-align: top;"|0.377

|-

|  style="vertical-align: top;"|Natural Gas Consumption  

|  style="vertical-align: top;"|0.636

|  style="vertical-align: top;"|0.190

|  style="vertical-align: top;"|-0.392

|  style="vertical-align: top;"|0.377

|-

|  style="vertical-align: top;"|Ren. Eng. Source Prod.

|  style="vertical-align: top;"|-0.128

|  style="vertical-align: top;"|0.190

|  style="vertical-align: top;"|-0.781

|  style="vertical-align: top;"|0.377

|-

|  style="border-bottom: 1pt solid black;vertical-align: top;"|Coal Production

|  style="border-bottom: 1pt solid black;vertical-align: top;"|-0.515

|  style="border-bottom: 1pt solid black;vertical-align: top;"|0.190

|  style="border-bottom: 1pt solid black;vertical-align: top;"|-0.694

|  style="border-bottom: 1pt solid black;vertical-align: top;"|0.377

|-

|  colspan='5'  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: top;"|Shapiro-Wilk: 0,961

Results of the regression model are given in Table 5. The value of the multiple determination coefficient (R Square) is relatively high and states that the model explains 52.3% of the dependent variable. The value of the standard error of the estimate (Std. Error of the Estimate) indicates that the set model is accurate, while the Durbin-Watson test indicates a positive autocorrelation (the result is less than 2), which is a good sign for our regression model.

'''Table 5.''' Multiple correlation, determination and autocorrelation coefficients.

{| style="width: 100%;border-collapse: collapse;"  

|-

|  colspan='7'  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|'''Model Summary^b'''

|  rowspan='2' style="border-top: 1pt solid black;"|R

|  rowspan='2' style="border-top: 1pt solid black;"|R Square

|  rowspan='2' style="border-top: 1pt solid black;"|Adjusted R Square

| rowspan='2' style="border-top: 1pt solid black;"|Std. error of the Estimate

| colspan='2'  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Change Statistics

|  style="border-top: 1pt solid black;vertical-align: bottom;"|Durbin-Watson

|-

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: bottom;"|R Square Change

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|F Change

| style="border-bottom: 1pt solid black;"|

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: top;"|0.723^a

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: top;"|0.523

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: top;"|0.507

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: top;"|1.37743

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: top;"|0.523

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: top;"|34.586

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|0.238

|-

|  colspan='7'  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: top;"|a. Predictors: (Constant), Coal Production, Natural Gas Consumption, Oil Price, R.E.S. Production, Natural Gas Production

b. Dependent Variable: Natural Gas Price

The ANOVA method was used to test the null hypothesis on the coefficient of multiple determinations. We have come to results that indicate that we can reject the null hypothesis i.e., it makes sense to use this model to explain the dependent variable (Table 6).

'''Table 6.''' Estimation of significance of partial regression coefficients.

{| style="width: 75%;border-collapse: collapse;"

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Model

| style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Sum of Squares

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Mean Square

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|F

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Sig.

|-

|  style="border-top: 1pt solid black;"|Regression

|  style="border-top: 1pt solid black;"|328.105

|  style="border-top: 1pt solid black;"|5

|  style="border-top: 1pt solid black;"|65.621

|  style="border-top: 1pt solid black;"|34.586

|  style="border-top: 1pt solid black;"|0.000

|-

|  style="border-bottom: 1pt solid black;"|Total

|  style="border-bottom: 1pt solid black;"|627.881

|  style="border-bottom: 1pt solid black;"|164

|  style="border-bottom: 1pt solid black;"|

|  style="border-bottom: 1pt solid black;"|

|  style="border-bottom: 1pt solid black;"|

The significance of partial regression coefficients was determined by performing a T-test. From Table 7. it is possible to conclude on the basis of coefficients in the column Sig. to make a unique contribution to the model, i.e. that the statistically significant variables “Crude Oil price” and “RES Production” (the same conclusion can be reached on basis of 95% confidence interval, which only in the case of the mentioned variables does not include 0). As values of the inflation factor of variance - VIF and the tolerance factor (Tol.) are within acceptable limits, we conclude that all variables can be part of the regression model, so the value of the independent variable Y is the sum of the values of the coefficient B other than zero.

'''Table 7.''' Estimation of significance of partial regression coefficients.

{| style="width: 100%;border-collapse: collapse;"  

|-

|  rowspan='2' style="border-top: 1pt solid black;"|

|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|(1)

|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|(2)

| rowspan='2' style="border-top: 1pt solid black;text-align: center;"|(3)

|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|(4)

|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|(5)

| colspan='2'  style="border-top: 1pt solid black;border-bottom: 1pt solid black;text-align: center;"|Collinearity Statistics

| rowspan='2' style="border-top: 1pt solid black;text-align: center;"|(6)

| rowspan='2' style="border-top: 1pt solid black;text-align: center;"|(7)

| Crude oil price

| Nat. Gas Production

| Nat. Gas Consumption

| RES Production

|  style="border-bottom: 1pt solid black;"|Coal Production

|  style="border-bottom: 1pt solid black;text-align: center;"|0.000

|  style="border-bottom: 1pt solid black;text-align: center;"|0.000

|  style="border-bottom: 1pt solid black;text-align: center;"|0.018

|  style="border-bottom: 1pt solid black;text-align: center;"|0.130

|  style="border-bottom: 1pt solid black;text-align: center;"|0.897

|  style="border-bottom: 1pt solid black;text-align: center;"|0.000

|  style="border-bottom: 1pt solid black;text-align: center;"|0.000

|  style="border-bottom: 1pt solid black;text-align: center;"|0.162

|  style="border-bottom: 1pt solid black;text-align: center;"|6.168

|  colspan='10'  style="border-top: 1pt solid black;border-bottom: 1pt solid black;vertical-align: top;"|(1) Unstandard Coefficients B, (2) Stand. Coefficients - Std. Error, (3) t – Beta, (4) Sig., (5) 95.0% Confidence Interval for B, (6) Tol., (7) VIF

Based on Table 7, natural gas price can be estimate using Eq. (12):

| '''Y (Natural Gas Price)''' =7,568 + 0,025 (Crude Oil Price) – 0,007 (RES Production)

|  style="text-align: right;width: 5px;text-align: right;white-space: nowrap;"|(12)

Based on values in Table 8, we can conclude that the homogeneity of variances and predictive values deviates from the limit values, so that in this case we have a pronounced heteroskedasticity.

'''Table 8.''' Heteroskedasticity tests

 

{| style="width: 61%;border-collapse: collapse;"  

|-

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Heteroskedasticity Test:

|  style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|Breusch-Pagan

| style="border-top: 1pt solid black;border-bottom: 1pt solid black;"|White

|  style="border-top: 1pt solid black;"|Critical value

|  style="border-top: 1pt solid black;"|3.8414588

|  style="border-top: 1pt solid black;"|5.9914645

|  style="border-bottom: 1pt solid black;"|Observed value*R-squared

|  style="border-bottom: 1pt solid black;"|16.1229036

|  style="border-bottom: 1pt solid black;"|20.6487180

As the influence of non-constant variance of errors on the efficiency of estimation by the least squares method as well as the validity of its conclusions, depends on several factors including sample size, degree of predictor variation, regressor values and the relationship between error variance and independent variables, it is not possible to reach full general conclusions relating to the consequences produced by heteroskedasticity in this case. Some authors believe that heteroskedasticity is not a big problem in econometric research. One of them is N. Gregori Mankiw who argues that “heteroskedasticity has never been a reason to reject an otherwise good model.” [38].

==8. Conclusions==

Obtained results on the connection and the influence of selected factors on the formation of the price of natural gas on the global market are generally in line with the existing results obtained by foreign authors. Investigating the period that includes two major shocks in the energy markets, we concluded that fluctuations in the price of certain energy sources as well as the volume of their production and consumption have a significant impact on the price of the observed energy source.

Natural gas is one of the most commonly used non-renewable hydrocarbons. Like almost any non-renewable energy source, it releases carbon dioxide during combustion. Therefore, one of the most important factors influencing prices of natural gas is green energy or energy obtained from renewable sources (solar energy, wind energy, etc.). Namely, the presence of this factor in the model is statistically significant with a high correlation coefficient with the price of natural gas - with a negative sign as the volume of natural gas production. Traditionally, a significant factor is the price of crude oil, which is statistically significant in the model and has a positive high correlation coefficient as well as coal production. Natural gas consumption has been identified as a factor that has a low correlation coefficient that cannot be a significant factor in long-term natural gas price forecasting.

Currently, one of the most important factors in forming the price of energy is the coronavirus, which strongly influences the price war and energy consumption. While household consumption increased due to lockdown policies and restrictions on movement, industrial consumption declined sharply. It is difficult to predict the expected volatility of natural gas prices in the future because factors of influence depend on global crises and shocks as well as on the geopolitical situation in the world. Investors in the natural gas market can use models formulated in this way to make investment decisions. Our findings highlight the importance of including pandemic risk in forecasting global gas supply and demand. The results of the research will help policymakers assess the impact of the COVID-19 pandemic on natural gas price volatility and formulate appropriate plans and strategies to reduce the impact and improve forecasting models that should include pandemics, natural and economic disasters.

==Funding==

This research has been supported by the Ministry of Education, Science, and Technological Development of the Republic of Serbia.

==Conflicts of interest==

 

The authors declare no conflict of interest. All authors have approved the final version of this paper.

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