Available online at www.HighTechJournal.org HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 346 ISSN: 2723-9535 The Global Equity Market Reactions of the Oil & Gas Midstream and Marine Shipping Industries to COVID-19: An Entropy Analysis Mina Nasiri 1, 2, Hamed Nasiri 1, 2, Saeid Nasiri 1, 2, Maliheh Bitarafan 1, Babak Fazelabdolabadi 3* 1 Adak Marine Shipping Company, No. 7, Azizollahi street, Mirzaye Shirazi Avenue, Tehran, Iran 2 Pacific Company, No. 7, Azizollahi street, Mirzaye Shirazi Avenue, Tehran, Iran 3 Research Institute of Petroleum Industry, Tehran, Iran Received 02 September 2021; Revised 14 November 2021; Accepted 23 November 2021; Published 01 December 2021 Abstract This article quantifies the information flow between major equities in the Oil & Gas Midstream and Marine Shipping industries, on the basis of the effective transfer entropy methodology. In addition, the article provides the first analysis of investor fear and market expectations in these sectors, according to the Rényi entropy approach. The period of study was extended over five years to fully capture the pre/post-COVID situations. The entropy results reveal a major change in the underlying information flow pattern among equities in the Oil & Gas Midstream and Marine Shipping sectors in the aftermath of COVID-19. According to the new (post-COVID) paradigm, the stocks in the Oil & Gas Midstream and Integrated Freight & Logistics industries have gained momentum in occupying six of the ten positions within the list of the most influential equities in the market, in terms of information transmission. The disorder and randomness have decreased for over 89% of the studied equities, after virus outbreak. For the equities detected with high information- transmission standing, the Rényi entropy results indicate that investors more likely showed a higher level of future expectations and a lower level of fear regarding frequent market events within the post-COVID timeline. Keywords: Marine Shipping; Logistics; Freight Transportation; COVID-19; Entropy. 1. Introduction The world has witnessed a different scenery since the emergence of the Coronavirus (COVID-19). One such major change has been the implementation of worldwide Non-Pharmaceutical Interventions (NPI) – mainly in the form of mandatory quarantines, business closures, and international travel restrictions – in order to control the spread of the virus. Although proven effective in reducing the rate of virus transmission [1, 2], the implementation of such large- scale containment measures has had negative economic consequences [3] which varies depending on their scale and severity of implementation. Among the repercussions of NPI, the diminishing international trade [4] - caused jointly by reduced production and market demand- should logically impact the transportation industry, in a sequel. As a matter of fact, the disruption in the global supply chain resulting from the COVID-19 emergence drove the transportation industry to a near halt [5], particularly during the early months of the crisis. A growing body of literature has focused on the impact of the COVID-19 issue on the marine transportation sector, in terms of performance [6-10] and equity market reactions [5]. For example, Xu et al. (2021) [6] conducted a * Corresponding author: bkfazel@yahoo.com http://dx.doi.org/10.28991/HIJ-2021-02-04-07  This is an open access article under the CC-BY license (https://creativecommons.org/licenses/by/4.0/). © Authors retain all copyrights. https://creativecommons.org/licenses/by/4.0/ https://orcid.org/0000-0003-0584-8177 HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 347 structural equation modelling analysis of confirmatory factor analysis and path assessment to study the impact of COVID-19 on the transportation and logistics sectors in China, and found a statistically insignificant correlation between COVID-19 and ocean freight in that country. Verschuur et al. (2021) [10] conducted an investigation on a global level and used the empirical vessel tracking information - as a high-frequency indicator of economic activity - to study the impact of NPI measures on maritime trade and found worldwide port-level trade losses, following the COVID-19 emergence, for which the ports in China, the Middle East, and Western Europe were detected with the largest absolute losses. Furthermore, it was estimated that the reduction in maritime trade became as low as -9.6% in the first eight months of the crisis [10]. With regards to the equity market reactions, Kamal et al. (2021) [5] applied an event study methodology to assess the market reactions of selected shipping stocks (listed on the New York Stock Exchange (NYSE)) to several COVID-related news of optimistic and pessimistic nature. They found positive market reactions for marine transportation equities to the announcement of optimistic events, such as approval of the first COVID-19 vaccine or the proposal of economic stimulus plans, and adverse market reactions to pessimistic news [11- 19]. However, the number of such investigations – linking COVID-19 and transportation equities-seem to be quite limited, compared to the existing bulk literature on the COVID-19 impacts on global equity markets [20-28]. As stock markets can be considered as a set of interconnected and correlated equities, it is conceivable that the internal force of the markets can be formed through the cumulative interactions of their listed firms [29-36]. As such, understanding the mutual information between equities should be important in analyzing the markets. However, such an information on connectivity (between equity participants) should be complemented by the information on the underlying directionality, in order to provide a complete image. Such a binary information set can be obtained by applying the concept of Transfer Entropy (TE), which is derived upon the formulation of conditional mutual information [37]. The transfer entropy methodology effectively quantifies the reduction in uncertainty – provided by past values of variables – in predicting the dependent variable, as it is conditioned on these past values, and is considered as a model-free statistic capable of measuring the time-directed transfer of information between stochastic variables as well as providing the asymmetric information transfer measures in multivariate distributions [37]. A number of previous investigations have applied the TE methodology to analyze the financial markets [11, 38, 39]. For instance, Golmohammadi & Fazelabdolabadi (2021) [11] mapped the information transfer paradigm between 2200 equities – globally distributed within major financial markets – for the periods before and after the COVID-19 outbreak. They report on drastic changes in major global equity markets in the aftermath of COVID-19 emergence, which was based on the changes in the underlying information flow pattern - derived from effective transfer entropy - within the markets studied [11] - Australia, Brazil, Canada, China, Germany, Iran, Japan, Qatar, Saudi Arabia, South Africa, South Korea, United Kingdom, and the United States. In addition, they report on substantial changes (nearly 70%) in the functionality of the market sectors – in terms of being a transmitter or receiver of information – encountered after COVID-19 emergence. Given the new circumstances that abound the global financial markets, it may be necessary to conduct an investigation to thoroughly understand the current standing of equities in the marine shipping and Oil & Gas midstream sectors. In this respect, the present work makes a two-fold contribution to the existing literature – providing the first information transfer map between equities in the marine shipping and Oil & Gas midstream sectors (in a cross-market domain) and quantifying the market expectations and investor fear for selected equities in these sectors. 2. Methods Used as the main processing stream in the present work, the method of transfer entropy, originally proposed by Schreiber (2000) [40], quantifies the asymmetric dynamics of two processes, using the conditional block entropy [41]. If the entropy is considered as a proxy to measure the uncertainty level inherent in optimally encoding the independent draws of a discrete random variable, the formulation of transfer entropy would be based on the premise of Shannon entropy [42]. Assuming 𝑋 as being a discrete random variable, with probability distribution function 𝑝(𝑥𝑡), the Shannon entropy, 𝐻𝑋, is defined as: 𝐻𝑋 = −𝛴𝑝(𝑥𝑡)𝑙𝑜𝑔2(𝑝(𝑥𝑡)) (1) If the random variable 𝑋 represents the event space of a time series, the sequence of its state outcomes until time 𝑡, with 𝑘 back steps in time, becomes: 𝑥𝑡 (𝑘) = 𝑥𝑡 , 𝑥𝑡−1, 𝑥𝑡−2, . . . , 𝑥𝑡−𝑘+1 (2) If we denote the probability of observing the variable in state 𝑥 at time 𝑡 + 1 as 𝑝(𝑥𝑡+1 ∨ 𝑥𝑡 (𝑘) ) = 𝑝(𝑥𝑡+1 ∨ 𝑥𝑡 , . . . , 𝑥𝑡−𝑘+1) then the average number of bits needed to encode the output state of the variable in time 𝑡 + 1 with known 𝑘backstep values – the entropy of 𝑥𝑡+1- can be written as: ℎ𝑋(𝑘) = −𝛴𝑝(𝑥𝑡+1, 𝑥𝑡 (𝑘) )𝑙𝑜𝑔2𝑝(𝑥𝑡+1 ∨ 𝑥𝑡 (𝑘) ) = 𝐻𝑋(𝑥𝑡+1, 𝑥𝑡 (𝑘) ) − 𝐻𝑋(𝑥𝑡 (𝑘) ) (3) HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 348 where the summation runs over all the possible values of (𝑥𝑡+1, 𝑥𝑡 (𝑘) ), for a fixed time 𝑡. The value of the calculated entropy hence depends on the selection of the block length 𝑘- referred to as conditional block entropy – which decreases along the increase in the length of the block, as long as 𝑥𝑡−𝑘contains more information to predict𝑥𝑡+1than 𝑥𝑡−𝑘+1 [41]. For a bi-variate case, the value of transfer entropy can be obtained by accounting the deviation from the generalized Markov property. Considering a time series 𝑌, the sequence of its observations until time 𝑡, with 𝑙 back steps in time, can be taken as: 𝑦𝑡 (𝑙) = 𝑦𝑡 , 𝑦𝑡−1, 𝑦𝑡−2, . . . , 𝑦𝑡−𝑙+1 (4) An information flow from process 𝑌 to process 𝑋 exists, if the information in 𝑦𝑡 (𝑙) can be valuable in forecasting 𝑥𝑡+1, despite the information collected from 𝑥𝑡 (𝑘) . The transfer entropy, 𝑇𝑌→𝑋(𝑘, 𝑙), is then formulated by Schreiber (2000) [40] as Equation 5, to subtract the information already contained in 𝑥𝑡 (𝑘) : 𝑇𝑌→𝑋(𝑘, 𝑙) = 𝛴 𝑥,𝑦 𝑝(𝑥𝑡+1, 𝑥𝑡 (𝑘) , 𝑦𝑡 (𝑙) )𝑙𝑜𝑔2𝑝(𝑥𝑡+1 ∨ 𝑥𝑡 (𝑘) , 𝑦𝑡 (𝑙) ) − 𝛴 𝑥 𝑝(𝑥𝑡+1, 𝑥𝑡 (𝑘) )𝑙𝑜𝑔2𝑝(𝑥𝑡+1 ∨ 𝑥𝑡 (𝑘) ) (5) 𝑇𝑌→𝑋(𝑘, 𝑙) = ℎ𝑋(𝑘) − ℎ𝑋,𝑌(𝑘. 𝑙) (6) where ℎ𝑋,𝑌(𝑘. 𝑙)denotes the conditional entropy of 𝑋, given the information of both 𝑥𝑡 (𝑘) and 𝑦𝑡 (𝑙) blocks. The results of the transfer entropy may be subject to bias, due to small-sample effects. To correct for this bias, it is suggested [43] to compute the effective transfer entropy, 𝐸𝑇𝐸𝑌→𝑋(𝑘, 𝑙), between the two processes. The effective transfer entropy is calculated by subtracting the value of transfer entropy obtained from Equation 5 from the value obtained after conducting a shuffling operation on process 𝑌, 𝑇𝑌𝑠ℎ𝑢𝑓𝑓𝑙𝑒𝑑→𝑋(𝑘, 𝑙). The shuffling procedure entails taking random draws from the distribution of 𝑌 and re-arrangement of the selected set to generate a new time series, in order to destroy statistical dependencies between the two processes as well as the time series dependencies of 𝑌 [42]: 𝐸𝑇𝐸𝑌→𝑋(𝑘, 𝑙) = 𝑇𝑌→𝑋(𝑘, 𝑙) − 𝑇𝑌𝑠ℎ𝑢𝑓𝑓𝑙𝑒𝑑→𝑋(𝑘, 𝑙) (7) 𝑇𝑌𝑠ℎ𝑢𝑓𝑓𝑙𝑒𝑑→𝑋(𝑘, 𝑙) → 0 as the sample size increases and becomes non-zero in case small-sample effects exist. The set of probability measures listed above are established over discretized values of the variables; therefore, the variables` data should be grouped into non-overlapping partitions, a priori. For this reason, the symbolic encoding scheme dominantly used would select the size of the bins, according to the 5% and 95% empirical quantiles of the data – 𝑞[0.05]and 𝑞[0.95]. As a result, the symbolically-encoded time series, 𝑠𝑡 , takes the following form: 𝑠𝑡 = { 1𝑓𝑜𝑟𝑦𝑡 ≤ 𝑞[0.05] 2𝑓𝑜𝑟𝑞[0.05] < 𝑦𝑡 < 𝑞[0.95] 3𝑓𝑜𝑟𝑦𝑡 ≥ 𝑞[0.95] } (8) To account for frequent and rare events, signal complexities were assessed by incorporating the Rényi entropy (as Equation 9) for each time series considered. 𝑅𝐸𝑑 = 1 1−𝑑 𝑙𝑜𝑔 (∑ 𝑝𝑖 𝑑 𝑖 ) (9) where 𝑑(𝑑 ≥ 0) represents the order of Rényi entropy, which favors rare events when 𝑑 < 1 and privileges frequents events as 𝑑 > 1 [44]. The estimation of the probabilities in Equation 9 was made through the Gaussian kernel functions. 3. Data Description The information used as input in the present study, is comprised of the closing daily prices of stocks of 70 companies, which presumably represent the main equities in the Oil & Gas Midstream and Marine Shipping sectors worldwide. The names of the companies selected are listed in Table 1. Such a name selection also ensures a cross- market inspection of the information transfer, as the equities are being traded in different financial markets. The input data was obtained from Yahoo Finance. The data was acquired for the time span between (2016-Aug-01 and 2021- Aug-01). This length was later divided into two periods, to account for prior/post-COVID timelines. The date used to set this division was taken to be 30-January-2020, on which the pandemic outbreak was officially declared by the World Health Organization [44]. HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 349 Table 1. The list of companies considered Index Company Name Yahoo ticker Industry 1 Ardmore Shipping Corporation ASC Marine Shipping 2 A.P. Møller - Mærsk A/S MAERSK-A.CO Marine Shipping 3 Badaro No. 19 Ship Investment Company 155900.KS Marine Shipping 4 Capital Product Partners L.P. CPLP Marine Shipping 5 COSCO Shipping Development Co., Ltd. 601866.SS Marine Shipping 6 COSCO Shipping Holdings Co., Ltd. 601919.SS Marine Shipping 7 Costamare Inc. CMRE Marine Shipping 8 Danaos Corporation DAC Marine Shipping 9 DHT Holdings, Inc. DHT Oil & Gas Midstream 10 Diana Shipping Inc. DSX Marine Shipping 11 Dorian LPG Ltd. LPG Oil & Gas Midstream 12 DSV Panalpina A/S DSV.CO Integrated Freight & Logistics 13 Dynagas LNG Partners LP DLNG Oil & Gas Midstream 14 Eagle Bulk Shipping Inc. EGLE Marine Shipping 15 Euronav NV EURN Oil & Gas Midstream 16 Euroseas Ltd. ESEA Marine Shipping 17 Evergreen Marine Corporation (Taiwan) Ltd. 2603.TW Marine Shipping 18 Frontline Ltd. FRO Oil & Gas Midstream 19 GasLog Partners LP GLOP Oil & Gas Midstream 20 Genco Shipping & Trading Limited GNK Marine Shipping 21 Global Ship Lease, Inc. GSL Marine Shipping 22 Globus Maritime Limited GLBS Marine Shipping 23 Golar LNG Limited GLNG Oil & Gas Midstream 24 Golden Ocean Group Limited GOGL Marine Shipping 25 Hamburger Hafen und Logistik Aktiengesellschaft HHFA.DE Marine Shipping 26 Hapag-Lloyd Aktiengesellschaft HLAG.DE Marine Shipping 27 HMM Co.,Ltd 011200.KS Marine Shipping 28 Höegh LNG Partners LP HMLP Oil & Gas Midstream 29 International Seaways, Inc. INSW Marine Shipping 30 Kawasaki Kisen Kaisha, Ltd. 9107.T Marine Shipping 31 Kirby Corporation KEX Marine Shipping 32 KNOT Offshore Partners LP KNOP Marine Shipping 33 Kuehne + Nagel International AG 0QMW.IL Integrated Freight & Logistics 34 Matson, Inc. MATX Marine Shipping 35 Mitsui O.S.K. Lines, Ltd. 9104.T Marine Shipping 36 Navigator Holdings Ltd. NVGS Oil & Gas Midstream 37 Navios Maritime Holdings Inc. NM Marine Shipping 38 Navios Maritime Partners L.P. NMM Marine Shipping 39 Nippon Yusen Kabushiki Kaisha 601018.SS Marine Shipping 40 Nippon Yusen Kabushiki Kaisha 9101.T Marine Shipping 41 Nordic American Tankers Limited NAT Marine Shipping 42 Overseas Shipholding Group, Inc. OSG Oil & Gas Midstream 43 Pangaea Logistics Solutions, Ltd. PANL Marine Shipping 44 PBF Logistics LP PBFX Oil & Gas Midstream 45 Pyxis Tankers Inc. PXS Marine Shipping 46 Qatar Gas Transport Company Limited QGTS.QA Oil & Gas Midstream 47 Qatar Navigation Q.P.S.C. QNNS.QA Marine Shipping 48 Regional Container Lines Public Company Limited RCL.BK Marine Shipping 49 Safe Bulkers, Inc. SB Marine Shipping 50 SEACOR Marine Holdings Inc. SMHI Marine Shipping 51 Seanergy Maritime Holdings Corp. SHIP Marine Shipping 52 SFL Corporation Ltd. SFL Marine Shipping 53 Shanghai International Port (Group) Co., Ltd. 600018.SS Marine Shipping HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 350 54 Sino-Global Shipping America, Ltd. SINO Integrated Freight & Logistics 55 Scorpio Tankers Inc. STNG Oil & Gas Midstream 56 Star Bulk Carriers Corp. SBLK Marine Shipping 57 StealthGas Inc. GASS Marine Shipping 58 Teekay Corporation TK Oil & Gas Midstream 59 Teekay LNG Partners L.P. TGP Oil & Gas Midstream 60 The National Shipping Company of Saudi Arabia 4030.SR Marine Shipping 61 Tidewater Inc. TDW Oil & Gas Midstream 62 Transportation and Logistics Systems, Inc. TLSS Integrated Freight & Logistics 63 Trencor Limited TRE.JO Marine Shipping 64 Tsakos Energy Navigation Limited TNP Oil & Gas Midstream 65 Top Ships Inc. TOPS Marine Shipping 66 U-Ming Marine Transport Corporation 2606.TW Marine Shipping 67 Wan Hai Lines Ltd. 2615.TW Marine Shipping 68 Westshore Terminals Investment Corporation WTE.TO Marine Shipping 69 XPO Logistics, Inc. XPO Integrated Freight & Logistics 70 Yang Ming Marine Transport Corporation 2609.TW Marine Shipping 4. Results and Discussion The effective transfer entropy was calculated, for each pair of the listed stocks (Table 1) along the both directions - 𝑋 → 𝑌 and 𝑌 → 𝑋. For each state in a given pair, the calculations were attempted over the periods, before and after the COVID-19 outbreak. The selection for the lag orders – 𝑘 and 𝑙-was taken as unity, which is an appropriate choice when analyzing the financial markets [42]. The number of shuffling operations performed was set to one hundred, to ensure efficient removal of bias from the established results. Figures 1 to 4 depict the computed results for the values of the effective transfer entropy for the companies considered. To ease its visual inspection, the results are presented separately for entries 1- 40 and 41-70 of the list (Table 1), as well as for the pre/post-COVID periods. With respect to the color interpretation of the results, a more positive number indicates more information transfer (from stock y to stock x) and zero is the case in which no information transfer has been detected, within the considered time span. The whole set of computed results for all the companies considered - including the transfer entropy, the effective transfer entropy and the corresponding statistical measures (standard deviations, p-values) – can be obtained from the corresponding author, upon reasonable request. Figure 1. The information flow (effective transfer entropy) from stock y to stock x, for the companies 1 through 40 (listed in Table 1), before the COVID-19 outbreak HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 351 Figure 2. The information flow (effective transfer entropy) from stock y to stock x, for the companies 41 through 70 (listed in Table 1), before the COVID-19 outbreak Figure 3. The information flow (effective transfer entropy) from stock y to stock x, for the companies 1 through 40 (listed in Table 1), after the COVID-19 outbreak HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 352 Figure 4. The information flow (effective transfer entropy) from stock y to stock x, for the companies 41 through 70 (listed in Table 1), after the COVID-19 outbreak The effective transfer entropy results show the formation of a new information transfer paradigm, after COVID-19 emergence, among major equities in the Oil & Gas Midstream and Marine Shipping sectors. According to our results, the new price action of equities acts more sensitively to each other (with few exceptions) and the overall information transfer in the two sectors has increased after COVID-19 outbreak, even in the devised cross-market domain. Given the market capitalization of the selected equities, a general extension of this finding to the post-COVID status of these two sectors is plausible. With respect to the information transmission, the market has seen an altered list of major players in the Oil & Gas Midstream and Marine Shipping sectors. As part of our analysis in the present paper, we have also studied the status of equities (in these sectors) with respect to their net information flow. An equity was then interpreted as being an information transmitter (receiver) if the net information outflow was positive (negative). In this context, a more positive net information outflow value rendered the equity as a holding a more influencing role in the market. Tables 2-3 list the main information transmitter equities in the Oil & Gas Midstream and Marine Shipping sectors, before and after COVID-19 respectively. As evident from the list, the Marine Shipping equities have lost grounds to other industries in the market, in the post-COVID timeline. This argument is based on the fact that six positions out of ten most influencing equities in these sectors were taken by the firms operating in the Oil & Gas Midstream and Integrated Freight & Logistics industries (Table 3) after COVID-19 emergence; namely, PBF Logistics LP; XPO Logistics, Inc; GasLog Partners LP; DSV Panalpina A/S; Transportation and Logistics Systems, Inc.; Kuehne + Nagel International AG. Table 2. The main information transmitter equities, before COVID-19 Rank Company name 1 Matson, Inc. 2 Navios Maritime Partners L.P. 3 Eagle Bulk Shipping Inc. 4 Tidewater Inc. 5 Star Bulk Carriers Corp. 6 Global Ship Lease, Inc. 7 Teekay LNG Partners L.P. 8 XPO Logistics, Inc. 9 Capital Product Partners L.P. 10 Navios Maritime Holdings Inc. HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 353 Table 3. The main information transmitter equities, after COVID-19 Rank Company name 1 PBF Logistics LP 2 XPO Logistics, Inc. 3 KNOT Offshore Partners LP 4 Hamburger Hafen und Logistik Aktiengesellschaft 5 GasLog Partners LP 6 Matson, Inc. 7 DSV Panalpina A/S 8 Global Ship Lease, Inc. 9 Transportation and Logistics Systems, Inc. 10 Kuehne + Nagel International AG In terms of market expectations and investor fear, the reactions have been mixed. Table 4 provides the net values of Rényi entropy for equities considered (Table 1), computed up to the order of 20. This net value was calculated as the Rényi entropy difference between the corresponding post/pre-COVID values. The results follow four distinct patterns, as described in Table 5. Table 4. The net values of Rényi entropy for equities listed in Table 1 d ASC MAERSK-A.CO 155900.KS CPLP 601866.SS 601919.SS CMRE DAC DHT DSX LPG DSV.CO DLNG EGLE EURN 2 -0.6788 0.6720 -0.0493 -0.1386 -0.2403 -0.2582 -0.3363 -0.6484 -0.5781 -0.8912 -1.0757 -0.1201 0.0611 -0.9214 0.3546 3 -0.6868 0.6740 -0.0322 -0.1537 -0.2287 -0.2435 -0.3361 -0.6506 -0.5901 -0.8913 -1.0631 -0.1151 0.0860 -0.9276 0.3802 4 -0.6884 0.6681 -0.0192 -0.1662 -0.2182 -0.2311 -0.3369 -0.6502 -0.5970 -0.8886 -1.0551 -0.1128 0.1018 -0.9282 0.3924 5 -0.6887 0.6621 -0.0094 -0.1752 -0.2082 -0.2212 -0.3361 -0.6488 -0.6011 -0.8850 -1.0506 -0.1109 0.1120 -0.9279 0.3988 6 -0.6889 0.6579 -0.0016 -0.1816 -0.1994 -0.2137 -0.3339 -0.6473 -0.6037 -0.8811 -1.0479 -0.1091 0.1189 -0.9277 0.4024 7 -0.6891 0.6555 0.0046 -0.1863 -0.1918 -0.2078 -0.3309 -0.6458 -0.6055 -0.8773 -1.0461 -0.1075 0.1238 -0.9276 0.4045 8 -0.6894 0.6545 0.0097 -0.1898 -0.1853 -0.2032 -0.3275 -0.6445 -0.6069 -0.8738 -1.0449 -0.1060 0.1273 -0.9276 0.4058 9 -0.6899 0.6544 0.0140 -0.1925 -0.1799 -0.1996 -0.3241 -0.6433 -0.6079 -0.8706 -1.0440 -0.1047 0.1299 -0.9278 0.4066 10 -0.6904 0.6546 0.0175 -0.1947 -0.1752 -0.1967 -0.3208 -0.6423 -0.6087 -0.8677 -1.0433 -0.1035 0.1320 -0.9281 0.4071 11 -0.6909 0.6551 0.0204 -0.1964 -0.1712 -0.1944 -0.3177 -0.6415 -0.6093 -0.8652 -1.0427 -0.1024 0.1336 -0.9285 0.4074 12 -0.6915 0.6556 0.0229 -0.1979 -0.1677 -0.1924 -0.3148 -0.6407 -0.6099 -0.8628 -1.0422 -0.1015 0.1349 -0.9289 0.4075 13 -0.6920 0.6561 0.0251 -0.1991 -0.1647 -0.1908 -0.3122 -0.6401 -0.6103 -0.8608 -1.0418 -0.1006 0.1359 -0.9293 0.4075 14 -0.6926 0.6565 0.0269 -0.2001 -0.1620 -0.1894 -0.3099 -0.6395 -0.6107 -0.8589 -1.0414 -0.0998 0.1368 -0.9297 0.4075 15 -0.6931 0.6568 0.0284 -0.2009 -0.1597 -0.1882 -0.3078 -0.6390 -0.6110 -0.8572 -1.0411 -0.0991 0.1376 -0.9301 0.4074 16 -0.6936 0.6570 0.0298 -0.2017 -0.1576 -0.1871 -0.3059 -0.6386 -0.6112 -0.8557 -1.0408 -0.0985 0.1382 -0.9305 0.4073 17 -0.6941 0.6572 0.0310 -0.2023 -0.1557 -0.1862 -0.3042 -0.6382 -0.6115 -0.8543 -1.0405 -0.0980 0.1388 -0.9309 0.4072 18 -0.6946 0.6573 0.0320 -0.2029 -0.1540 -0.1854 -0.3027 -0.6378 -0.6117 -0.8531 -1.0402 -0.0975 0.1393 -0.9313 0.4071 19 -0.6951 0.6574 0.0329 -0.2034 -0.1525 -0.1847 -0.3013 -0.6375 -0.6119 -0.8519 -1.0399 -0.0970 0.1397 -0.9317 0.4069 20 -0.6955 0.6574 0.0337 -0.2039 -0.1511 -0.1840 -0.3001 -0.6372 -0.6120 -0.8509 -1.0397 -0.0966 0.1401 -0.9320 0.4068 d ESEA 2603.TW FRO GLOP GNK GSL GLBS GLNG GOGL HHFA.DE HLAG.DE 011200.KS HMLP INSW 9107.T 2 -0.0294 -0.9770 -1.0645 -0.1719 -0.0075 -0.0746 -0.5744 -0.8612 -0.8747 -0.1452 -0.3016 -1.7171 0.3408 -0.2256 -1.1076 3 -0.0537 -0.9732 -1.0994 -0.1937 -0.0226 -0.0937 -0.6026 -0.8521 -0.9236 -0.1342 -0.3198 -1.7440 0.3574 -0.1946 -1.0807 4 -0.0693 -0.9692 -1.1165 -0.2095 -0.0306 -0.1130 -0.6132 -0.8461 -0.9459 -0.1212 -0.3339 -1.7570 0.3668 -0.1812 -1.0612 5 -0.0783 -0.9665 -1.1270 -0.2213 -0.0344 -0.1276 -0.6173 -0.8415 -0.9577 -0.1110 -0.3444 -1.7654 0.3734 -0.1740 -1.0470 6 -0.0840 -0.9652 -1.1343 -0.2306 -0.0360 -0.1380 -0.6188 -0.8378 -0.9646 -0.1036 -0.3523 -1.7718 0.3785 -0.1694 -1.0362 7 -0.0878 -0.9646 -1.1397 -0.2380 -0.0366 -0.1454 -0.6192 -0.8349 -0.9690 -0.0981 -0.3585 -1.7770 0.3825 -0.1660 -1.0278 8 -0.0906 -0.9645 -1.1441 -0.2441 -0.0366 -0.1510 -0.6190 -0.8324 -0.9720 -0.0941 -0.3635 -1.7813 0.3857 -0.1634 -1.0210 9 -0.0926 -0.9647 -1.1476 -0.2492 -0.0363 -0.1552 -0.6185 -0.8304 -0.9740 -0.0911 -0.3676 -1.7850 0.3882 -0.1612 -1.0153 10 -0.0943 -0.9650 -1.1505 -0.2535 -0.0359 -0.1586 -0.6181 -0.8286 -0.9755 -0.0887 -0.3710 -1.7882 0.3903 -0.1593 -1.0106 11 -0.0956 -0.9655 -1.1529 -0.2572 -0.0354 -0.1613 -0.6176 -0.8271 -0.9767 -0.0868 -0.3738 -1.7910 0.3921 -0.1577 -1.0065 12 -0.0967 -0.9661 -1.1550 -0.2603 -0.0348 -0.1635 -0.6171 -0.8258 -0.9775 -0.0853 -0.3762 -1.7935 0.3936 -0.1562 -1.0030 HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 354 13 -0.0976 -0.9666 -1.1568 -0.2630 -0.0343 -0.1654 -0.6167 -0.8246 -0.9782 -0.0841 -0.3782 -1.7956 0.3949 -0.1549 -0.9999 14 -0.0984 -0.9672 -1.1583 -0.2654 -0.0338 -0.1670 -0.6164 -0.8235 -0.9787 -0.0830 -0.3799 -1.7975 0.3960 -0.1537 -0.9972 15 -0.0991 -0.9677 -1.1596 -0.2675 -0.0332 -0.1684 -0.6160 -0.8225 -0.9792 -0.0822 -0.3814 -1.7992 0.3970 -0.1527 -0.9947 16 -0.0997 -0.9682 -1.1608 -0.2694 -0.0328 -0.1696 -0.6158 -0.8217 -0.9795 -0.0814 -0.3827 -1.8008 0.3978 -0.1517 -0.9926 17 -0.1002 -0.9687 -1.1618 -0.2711 -0.0323 -0.1706 -0.6155 -0.8209 -0.9798 -0.0808 -0.3838 -1.8021 0.3986 -0.1508 -0.9906 18 -0.1006 -0.9692 -1.1627 -0.2726 -0.0318 -0.1715 -0.6153 -0.8201 -0.9801 -0.0802 -0.3848 -1.8034 0.3993 -0.1500 -0.9888 19 -0.1010 -0.9697 -1.1636 -0.2739 -0.0314 -0.1724 -0.6151 -0.8195 -0.9803 -0.0797 -0.3857 -1.8045 0.3999 -0.1492 -0.9871 20 -0.1014 -0.9701 -1.1643 -0.2751 -0.0310 -0.1731 -0.6149 -0.8188 -0.9805 -0.0793 -0.3865 -1.8055 0.4004 -0.1485 -0.9856 d KEX KNOP 0QMW.IL MATX 9104.T NVGS NM NMM 601018.SS 9101.T NAT OSG PANL PBFX PXS 2 -0.8968 -0.3180 -0.2867 -0.6232 -0.4708 -0.3577 -0.4931 -0.1950 -0.7546 -0.4587 -0.1042 -0.2364 -1.8282 -0.6702 -0.9108 3 -0.9257 -0.2267 -0.3022 -0.6237 -0.4865 -0.3494 -0.4769 -0.1786 -0.7596 -0.4377 -0.1207 -0.2067 -1.8379 -0.6561 -0.9382 4 -0.9383 -0.1675 -0.3093 -0.6217 -0.4916 -0.3447 -0.4689 -0.1689 -0.7597 -0.4215 -0.1270 -0.1914 -1.8353 -0.6485 -0.9482 5 -0.9446 -0.1285 -0.3137 -0.6196 -0.4932 -0.3416 -0.4645 -0.1623 -0.7586 -0.4095 -0.1297 -0.1833 -1.8307 -0.6433 -0.9522 6 -0.9482 -0.1018 -0.3171 -0.6175 -0.4934 -0.3393 -0.4617 -0.1574 -0.7571 -0.4003 -0.1309 -0.1789 -1.8264 -0.6394 -0.9536 7 -0.9503 -0.0829 -0.3198 -0.6156 -0.4931 -0.3374 -0.4599 -0.1536 -0.7556 -0.3930 -0.1314 -0.1766 -1.8226 -0.6362 -0.9538 8 -0.9516 -0.0690 -0.3220 -0.6138 -0.4926 -0.3359 -0.4585 -0.1507 -0.7541 -0.3871 -0.1316 -0.1753 -1.8193 -0.6337 -0.9536 9 -0.9526 -0.0584 -0.3239 -0.6122 -0.4922 -0.3345 -0.4574 -0.1483 -0.7528 -0.3823 -0.1317 -0.1746 -1.8165 -0.6316 -0.9531 10 -0.9532 -0.0501 -0.3255 -0.6107 -0.4917 -0.3334 -0.4566 -0.1464 -0.7515 -0.3782 -0.1317 -0.1742 -1.8141 -0.6299 -0.9526 11 -0.9536 -0.0435 -0.3269 -0.6094 -0.4914 -0.3324 -0.4559 -0.1448 -0.7504 -0.3747 -0.1318 -0.1739 -1.8120 -0.6284 -0.9520 12 -0.9539 -0.0381 -0.3281 -0.6081 -0.4911 -0.3314 -0.4553 -0.1435 -0.7493 -0.3717 -0.1319 -0.1738 -1.8102 -0.6271 -0.9514 13 -0.9541 -0.0336 -0.3291 -0.6071 -0.4909 -0.3306 -0.4548 -0.1425 -0.7483 -0.3691 -0.1319 -0.1737 -1.8086 -0.6259 -0.9509 14 -0.9542 -0.0298 -0.3300 -0.6061 -0.4907 -0.3299 -0.4544 -0.1415 -0.7473 -0.3669 -0.1320 -0.1737 -1.8072 -0.6249 -0.9504 15 -0.9542 -0.0266 -0.3308 -0.6052 -0.4905 -0.3292 -0.4540 -0.1408 -0.7464 -0.3648 -0.1322 -0.1736 -1.8059 -0.6241 -0.9499 16 -0.9543 -0.0238 -0.3316 -0.6044 -0.4904 -0.3286 -0.4537 -0.1401 -0.7456 -0.3630 -0.1323 -0.1736 -1.8047 -0.6233 -0.9495 17 -0.9543 -0.0213 -0.3322 -0.6038 -0.4903 -0.3281 -0.4534 -0.1395 -0.7448 -0.3614 -0.1324 -0.1736 -1.8037 -0.6226 -0.9491 18 -0.9542 -0.0192 -0.3328 -0.6031 -0.4902 -0.3276 -0.4531 -0.1390 -0.7441 -0.3600 -0.1325 -0.1736 -1.8028 -0.6220 -0.9488 19 -0.9542 -0.0173 -0.3333 -0.6026 -0.4901 -0.3271 -0.4529 -0.1385 -0.7434 -0.3587 -0.1327 -0.1736 -1.8019 -0.6214 -0.9485 20 -0.9542 -0.0156 -0.3338 -0.6021 -0.4900 -0.3267 -0.4527 -0.1382 -0.7427 -0.3575 -0.1328 -0.1736 -1.8012 -0.6209 -0.9482 d QGTS.QA QNNS.QA RCL.BK SB SMHI SHIP SFL 600018.SS SINO STNG SBLK GASS TK TGP 4030.SR 2 -0.8535 -0.2035 -1.0008 -0.7749 -0.2061 -1.2914 -0.3213 0.3290 -0.8943 -0.6042 -0.6108 -0.8985 -0.7367 -1.1938 0.1466 3 -0.8763 -0.1821 -1.0301 -0.8002 -0.1862 -1.2813 -0.3017 0.3488 -0.8868 -0.6078 -0.6245 -0.8829 -0.7395 -1.2281 0.1994 4 -0.8864 -0.1704 -1.0495 -0.8121 -0.1764 -1.2751 -0.2919 0.3624 -0.8784 -0.6082 -0.6277 -0.8754 -0.7373 -1.2459 0.2295 5 -0.8903 -0.1630 -1.0637 -0.8192 -0.1712 -1.2718 -0.2863 0.3722 -0.8709 -0.6074 -0.6274 -0.8717 -0.7347 -1.2571 0.2489 6 -0.8913 -0.1578 -1.0745 -0.8241 -0.1682 -1.2700 -0.2829 0.3797 -0.8644 -0.6062 -0.6257 -0.8699 -0.7323 -1.2648 0.2624 7 -0.8911 -0.1537 -1.0829 -0.8277 -0.1663 -1.2692 -0.2807 0.3857 -0.8588 -0.6049 -0.6235 -0.8692 -0.7302 -1.2703 0.2722 8 -0.8905 -0.1503 -1.0896 -0.8303 -0.1648 -1.2689 -0.2792 0.3906 -0.8540 -0.6039 -0.6212 -0.8691 -0.7284 -1.2745 0.2796 9 -0.8897 -0.1473 -1.0951 -0.8324 -0.1636 -1.2690 -0.2780 0.3948 -0.8498 -0.6030 -0.6190 -0.8694 -0.7269 -1.2777 0.2854 10 -0.8889 -0.1446 -1.0996 -0.8340 -0.1625 -1.2692 -0.2772 0.3984 -0.8462 -0.6022 -0.6169 -0.8698 -0.7255 -1.2801 0.2899 11 -0.8882 -0.1421 -1.1034 -0.8353 -0.1615 -1.2694 -0.2765 0.4016 -0.8429 -0.6016 -0.6150 -0.8704 -0.7244 -1.2821 0.2936 12 -0.8875 -0.1398 -1.1066 -0.8363 -0.1606 -1.2698 -0.2760 0.4045 -0.8401 -0.6011 -0.6132 -0.8710 -0.7234 -1.2838 0.2966 13 -0.8869 -0.1378 -1.1094 -0.8372 -0.1597 -1.2701 -0.2756 0.4071 -0.8375 -0.6007 -0.6116 -0.8716 -0.7226 -1.2851 0.2991 14 -0.8864 -0.1359 -1.1118 -0.8379 -0.1589 -1.2704 -0.2752 0.4094 -0.8352 -0.6003 -0.6101 -0.8723 -0.7219 -1.2862 0.3012 15 -0.8859 -0.1342 -1.1139 -0.8385 -0.1581 -1.2707 -0.2748 0.4115 -0.8331 -0.6001 -0.6087 -0.8729 -0.7212 -1.2871 0.3030 16 -0.8855 -0.1326 -1.1158 -0.8390 -0.1574 -1.2710 -0.2745 0.4135 -0.8312 -0.5998 -0.6075 -0.8735 -0.7207 -1.2879 0.3046 17 -0.8851 -0.1312 -1.1175 -0.8394 -0.1567 -1.2713 -0.2743 0.4153 -0.8294 -0.5997 -0.6063 -0.8741 -0.7203 -1.2886 0.3059 18 -0.8848 -0.1299 -1.1189 -0.8398 -0.1561 -1.2716 -0.2740 0.4169 -0.8278 -0.5995 -0.6053 -0.8747 -0.7199 -1.2892 0.3071 19 -0.8844 -0.1287 -1.1203 -0.8401 -0.1555 -1.2718 -0.2738 0.4185 -0.8263 -0.5994 -0.6043 -0.8752 -0.7195 -1.2897 0.3082 20 -0.8842 -0.1276 -1.1215 -0.8404 -0.1549 -1.2720 -0.2736 0.4199 -0.8250 -0.5993 -0.6034 -0.8757 -0.7192 -1.2902 0.3091 HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 355 d TDW TLSS TRE.JO TNP TOPS 2606.TW 2615.TW WTE.TO XPO 2 0.6381 -1.0532 -1.0342 -0.7370 -0.4566 -0.0280 -0.7126 -0.4532 0.1706 3 0.5966 -1.0509 -1.0426 -0.7396 -0.4728 -0.0375 -0.7313 -0.4639 0.1895 4 0.5614 -1.0505 -1.0447 -0.7474 -0.4772 -0.0472 -0.7408 -0.4659 0.1895 5 0.5347 -1.0500 -1.0461 -0.7539 -0.4779 -0.0528 -0.7464 -0.4655 0.1881 6 0.5147 -1.0494 -1.0474 -0.7585 -0.4776 -0.0559 -0.7500 -0.4645 0.1876 7 0.4995 -1.0488 -1.0487 -0.7615 -0.4770 -0.0575 -0.7525 -0.4634 0.1879 8 0.4877 -1.0483 -1.0498 -0.7635 -0.4764 -0.0584 -0.7542 -0.4624 0.1887 9 0.4784 -1.0479 -1.0507 -0.7648 -0.4759 -0.0588 -0.7555 -0.4616 0.1896 10 0.4708 -1.0475 -1.0515 -0.7657 -0.4755 -0.0590 -0.7564 -0.4610 0.1906 11 0.4647 -1.0472 -1.0522 -0.7663 -0.4752 -0.0590 -0.7572 -0.4605 0.1917 12 0.4595 -1.0470 -1.0527 -0.7668 -0.4750 -0.0590 -0.7577 -0.4601 0.1926 13 0.4551 -1.0468 -1.0531 -0.7671 -0.4748 -0.0588 -0.7582 -0.4599 0.1935 14 0.4514 -1.0467 -1.0535 -0.7673 -0.4747 -0.0587 -0.7586 -0.4597 0.1944 15 0.4482 -1.0466 -1.0538 -0.7675 -0.4746 -0.0586 -0.7590 -0.4597 0.1951 16 0.4454 -1.0465 -1.0541 -0.7676 -0.4745 -0.0584 -0.7592 -0.4597 0.1958 17 0.4429 -1.0464 -1.0543 -0.7677 -0.4745 -0.0583 -0.7595 -0.4597 0.1965 18 0.4407 -1.0463 -1.0545 -0.7678 -0.4744 -0.0581 -0.7597 -0.4598 0.1971 19 0.4388 -1.0462 -1.0547 -0.7678 -0.4744 -0.0580 -0.7599 -0.4599 0.1976 20 0.4370 -1.0462 -1.0549 -0.7679 -0.4744 -0.0578 -0.7601 -0.4601 0.1981 Table 5. Description of different patterns detected in Rényi entropy outputs Pattern Description I Randomness and disorder has decreased in the post-COVID timeline. The level of information disorder in frequent events has increased during the pandemic, which indicates that investors showed higher level of fear and lower level of future expectations regarding most frequent events. II Randomness and disorder has decreased in the post-COVID timeline. The level of information disorder in frequent events has decreased during the pandemic, which indicates that investors showed lower level of fear and higher level of future expectations regarding most frequent events. III Randomness and disorder has increased in the post-COVID timeline. The level of information disorder in frequent events has increased during the pandemic, which indicates that investors showed higher level of fear and lower level of future expectations regarding most frequent events. IV Randomness and disorder has increased in the post-COVID timeline. The level of information disorder in frequent events has decreased during the pandemic, which indicates that investors showed lower level of fear and higher level of future expectations regarding most frequent events. For the majority of the equities considered (over 89%), the randomness and disorder have decreased since the pandemic. The investors' expectations and level of fear for this group, however, were evenly distributed. In other words, for the most frequent events in the market, investors showed both lower/higher level of future expectations. Table 6 reports the equities according to their detected pattern. In the most influential stocks (Table 3), the Rényi entropy pattern belonged to group II (Table 4), which indicates that investors had shown a lower level of fear regarding frequent market events in these equities in the post-COVID timeline. Table 6. The affiliated stocks to each Rényi entropy pattern Pattern Affiliated Stocks I CMRE; DAC; LPG; DSV.CO; GLNG; INSW; KNOP; MATX; NVGS; NM; NMM; OSG; PXS; QNNS.QA; SMHI; SHIP; SFL; SINO; STNG; GASS; TK; TRE.JO; WTE.TO; 2603.TW; 601018.SS; 601866.SS; 601919.SS; 9101.T; 9107.T. II ASC; CPLP; DHT; DSX; EGLE; ESEA; FRO; GLOP; GNK; GSL; GLBS; GOGL; HHFA.DE; HLAG.DE; KEX; NAT; PANL; PBFX; QGTS.QA; TCL.BK; TLSS; SB; SBLK; TGP; TNP; TOPS; 0QMW.IL; 011200.KS; 2606.TW; 2615.TW; 9104.T. III DLNG; EURN; HMLP; XPO; 155900.KS; 4030.SR ; 600018.SS. IV MAERSK-A.CO; TDW. HighTech and Innovation Journal Vol. 2, No. 4, December, 2021 356 5. Conclusion The entropy analysis of equities in the Oil & Gas Midstream and Marine Shipping sectors reveals changes in their underlying information flow patterns since the emergence of the COVID-19 virus. The post-COVID market action of equities in these two sectors behaves more sensitively to each other, as deducted from the effective transfer entropy results. According to the new (post-COVID) paradigm, the stocks in the Oil & Gas Midstream and Integrated Freight & Logistics industries have gained momentum in occupying six of the ten positions on the list of the most influential equities in the market, in terms of information transmission. The disorder and randomness has generally decreased for the studied equities after the COVID-19 emergence. Investors’ fears and future market expectations for the studied equities are found to be mixed. Nevertheless, the Rényi entropy results indicate that investors more likely showed a lower level of fear regarding frequent market events in equities possessing high information transmission status in the market. 6. Declarations 6.1. Author Contributions All authors have equally contributed towards Conceptualization, methodology, formal analysis, investigation, resources, writing—original draft preparation, writing—review and editing, visualization. All authors have read and agreed to the published version of the manuscript. 6.2. Data Availability Statement The data presented in this study are available in article. 6.3. Funding The authors received no financial support for the research, authorship, and/or publication of this article. 6.4. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 7. References [1] Hsiang, S., Allen, D., Annan-Phan, S., Bell, K., Bolliger, I., Chong, T., Druckenmiller, H., Huang, L. Y., Hultgren, A., Krasovich, E., Lau, P., Lee, J., Rolf, E., Tseng, J., & Wu, T. (2020). The effect of large-scale anti-contagion policies on the COVID-19 pandemic. Nature, 584(7820), 262–267. doi:10.1038/s41586-020-2404-8. [2] Chinazzi, M., Davis, J. 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