**1. Introduction**

The natural gas market has registered an expanding trend, because the fuel transition from coal to natural gas is accelerating in both the industrial and power sectors to reduce greenhouse gas emissions and prevent air pollution, as well as stagnant nuclear power generation. According to BP Statistical Review of World Energy June 2019 [1], the total primary energy consumption in the world grew from 12.4 billion tonnes of oil equivalent (btoe) in 2011 to 13.9 btoe in 2018. Coal consumption was almost constant at 3.6 btoe, while natural gas consumption increased from 2.8 btoe to 3.3 btoe. As a result, the composition ratio of natural gas increased from 22.4% to 23.9%, though the composition ratio of coal decreased from 30.5% to 27.2%. Besides the traditional gas-producing countries in the Middle East and Southeast Asia, others have been increasing their presence as exporting countries, such as Australia (which has been developing large-scale gas wells, including unconventional gas fields) and the United States of America (USA) (which began to export liquefied natural gas (LNG) derived from shale gas). Furthermore, the development of gas fields has been promoted even in Africa recently. Natural gas production skyrocketed from 28 million tonnes of oil equivalent (mtoe), 457 mtoe, and 120 mtoe in 2011 to 112 mtoe, 715 mtoe, and 203 mtoe in 2018, in Australia, the USA, and all of Africa, respectively. On the other hand, consumption is skyrocketing in China and the Middle East, in addition to steady consumption for the members of the Organisation for Economic Co-operation and Development (OECD). Natural gas consumption increased from 24 mtoe, 168 mtoe, and 1142 mtoe in 2011 to 243 mtoe, 476 mtoe, and 1505 mtoe in 2018 in China, all of the Middle East, and the OECD countries.

In the European market, progress in the deregulation of gas business and the decreasing trend of the proportion of long-term contracts linked to crude oil prices has been activating an inter-market arbitrage based on gas pipelines. Moreover, in the global market, the increase in the ratio of LNG to

total natural gas trading volumes, the accelerated removal of the destination restriction clause from LNG sales contracts, and the decreasing trend for the percentage of long-term contracts linked to crude oil prices are activating an intercontinental arbitrage based on LNG. As the proportion of spot trading increases, the liquidity of the natural gas market also increases significantly.

According to the Japan Fair Trade Commission of the Government of Japan [2], the natural gas market has not been flexible in terms of region, volume, and price, with the supply chain being considered a special energy market. However, as the trading volume increases with the increase in the number of producing and/or consuming countries, gas market liquidity has also become higher. As a result, the market is changing to a general commodity market.

Natural gas portfolio holders require both security and flexibility in terms of demand and supply because they have to invest heavily and trade globally. Therefore, they need to monitor the relationship between international natural gas markets in terms of revenue and risk management. As such, we adopt the spillover index developed by Diebold and Yilmaz [3] to measure return and volatility spillovers between natural gas price indexes in Europe, North America, and Asia Pacific.

Our expectations for measuring spillover e ffects between markets are twofold. First, we can easily grasp the potential of a portfolio with a single index obtained by analyzing the relationship of return and volatility between securities that make up that portfolio. We can also overview the potential downside risk of the portfolio without strictly measuring the value at risk and the expected shortfall by a Monte Carlo simulation. Second, we can respond to risks early by using the index as a predictive risk indicator. If we monitor the market that is the source of the spillover, investors can smoothly rebalance their portfolios.

We must test the stationarity of variables because Diebold and Yilmaz [3] develop the spillover index based on the vector moving average (VMA) representation of the vector autoregression (VAR) model. However, the approach proposed by Diebold and Yilmaz [3] is not the Granger–causality test, but just the quantification of the spillover e ffect. In other words, this technique does not assess whether significant information to predict returns and/or volatility exists, but only estimates how the variables are mutually influential.

However, notwithstanding these limitations of the method, we can obtain not only academic findings concerning the most remarkable transformation market, that is, the natural gas and LNG markets, but also useful information for practitioners, such as regulatory authorities, exchanges, consumers, and suppliers. Further, this index is extremely informative for long-term investment, daily trading, production, and risk managemen<sup>t</sup> in operating companies that hold such a natural gas portfolio.

In recent years, there have been increased studies on the natural gas market in the context of de-CO2, the shale gas revolution, and increased liquidity. Kum et al. [4], Das et al. [5], and Bildirici and Bakirtas [6] examine the relationship between natural gas consumption volume and macroeconomic indicators in major developed countries, emerging national economies, and a developing country. Acaravci et al. [7] investigates the relationship between natural gas prices and stock prices in European countries. Nakajima and Hamori [8], Atil et al. [9], Perifanis et al. [10], Tiwari et al. [11], and Xia et al. [12] analyze the relationship between natural gas prices and the other energy prices in the USA. Batten et al. [13] study the relationship between Russian natural gas prices and other energy prices. These previous studies were conducted in the context of causality, spillover, and market integration between natural gas and other economic variables. Moreover, Nakajima [14] argues whether profits can be earned by statistical arbitrage between wholesale electricity futures and natural gas futures.

However, few studies have examined natural gas market integration. Olsen et al. [15], Scarcio ffolo and Etienne [16], and Ren et al. [17] discuss the market integration in North America. Nick [18], Osiˇcka et al. [19], and Bastianin et al. [20] examine the European natural gas market integration. Shi et al. [21] reveals the interrelationship of LNG prices in Asia. Furthermore, there are few studies that have investigated the natural gas market integration across several regions. Neumann [22] studies the relationship between European and North American markets. Chai et al. [23] study the relationship

between the Chinese and the global market. No research has examined the global natural gas market integration, with the exception of that by Silverstovs et al. [24], analyzing the cointegrated relationship between North America, Europe, and Japan based on monthly data from before the shale gas revolution. No studies analyze the spillover e ffects between North American, European, and Asia-Pacific natural gas markets based on daily data.

We adopt Diebold and Yilmaz's [3] approach to examine spillovers between global natural gas price indexes based on daily data. The correlation coe fficient captures only phenomena that do not include the meaning of the relationship. Although the cointegration analysis and the Granger causality test lead to long-term equilibrium and forecast performance, it is di fficult to grasp the whole picture at a glance in the case of many variables to be analyzed. Diebold and Yilmaz's [3] approach captures not only pairwise connectedness but also total connectedness. Although Diebold and Yilmaz's [3] approach is not suitable for dynamic descriptions such as multivariate generalized autoregressive conditional heteroscedasticity (GARCH), it is possible to capture dynamic trends with moving window samples. Moreover, we spectrally decompose the Diebold and Yilmaz [3] index by Fourier transform. Baruník and Kˇrehlík [25] utilized the same technique for the first time and later papers applied this approach to the energy market. For instance, Toyoshima and Hamori [26] measure the spillover index for global crude oil markets and decompose it into long-, medium-, and short-term factors. Ji et al. [27] examine the spillover e ffects between crude oil, heating oil, gasoline, and natural gas in North America and the United Kingdom.

Our contribution to the literature is threefold. The contributions of this paper relate to clarifying the relationships by measuring the connectedness and its frequency dynamics in the global gas market. First, we indicate no progressing integration of the global natural gas market, although we indicate the strong spillover e ffect between European markets. Moreover, we indicate that the volatility is higher integrated than returns. The Diebold and Yilmaz's [3] approach indicates that the total connectedness of return and volatility is 22.9% and 32.8%, respectively, while each total connectedness is mostly dependent on the pairwise connectedness between European natural gas price indexes. Second, our spectral analyses indicate that long-term factors contribute to volatility spillovers, while short-term factors contribute to return spillovers. We argue that arbitrage might cause short-term return spillovers and long-term memory of volatility might cause long-term volatility spillovers. Finally, our rolling analyses indicate that the above two characteristics continue. Moreover, we argue that regional climate, demand and supply, and incidents might make spillover e ffects larger or smaller.

The remainder of this paper is organized as follows. Section 2 describes the analyzed data, summary statistics, and preliminary basic analyses. Section 3 explains the adopted methodology. Section 4 presents the empirical results. Section 5 provides a summary of the findings and states conclusions.

#### **2. Data and Preliminary Analyses**
