“…In particular, in empirical analysis, some key characters of the regional natural gas markets, e.g., features of the underground pipeline network, may not all be available to be considered, and empirical challenges hence arise as these unconsidered features are likely to be spatially correlated (c.f., Cuddington and Wang, 2006;Park et al, 2008;Arano and Velikova, 2009). Vector time series analysis and the pair-wise approach have often been adopted in analysing the integrations of regional energy markets in the literature (c.f., De Vany and Walls, 1993;Pesaran, 2007;Holmes et al, 2013). For example, De Vany and Walls (1993) used cointegration method to investigate the integrations by considering one hundred and ninety market pairs among twenty spatially separated natural gas markets in the U.S.. Park et al (2008) considered the relationships in mean among a relatively small number of eight North American natural gas spot markets by combining the advances in causal flow analysis with vector time series analysis.…”