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The literature concerning energy price expectation, volatility characteristics, and persistence is extensive. In terms of price learning expectation, it presumes that the public know the energy price prediction model, but they do not know the parameters of the model exactly, and thus estimate the unknown parameters according to the newest information they can obtain at the time. Milani (2005) examines learning expectation from the viewpoint of the influences of the learning speed on the inflation expectation and the best speed. Milani (2007) compares the learning expectation with the rational expectation using the DSGE model and argues that learning can enhance the model fitting effect. Fan and Gao (2016) investgate the adaptive learning expectation of Chinese inflation and examine empirically the roles of inflation expectation and persitence on equilibrium inflation. Recently, machine learnings are also researched deeply. Zhu et al. (2022a) invetigate the ability of the opposition-based learning salp swarm algorithm in price prediction and Zhu et al. (2022b) invetigate the classification ability of extreme learning machines (ELMs) with rapid learning rates.
Second, regarding the volatility characteristics and the spillover effect between different countries, under no arbitrage, the volatility of prices is equal to that of information flow (Ross, 1989). With the integration of the world economics and the intensification of globalization, volatility and its spillover between different countries’ financial markets, especially in the asset portfolio construction, and how the volatility setting influences the market information flow and its transmission among different markets are of great significance (Huang, 2012; Song et al., 2020). Using the GARCH model, Pindyck (2004) investgates the price volatility of American oil and gas. Huang (2012) adopts the bivariate GARCH model to examine the volatility of different countries’ stock index futures markets. GARCH volatility models set the conditional variance as the function of the variable’s past value. On the other hand, stochastic volatility models introduce the error term into the conditional variance and thus not only does the variance have stochastic characteristics, but the model flexibility is also greatly increased (Asai and et al., 2006). Asai et al. (2006) conduct a systematic literature review on multivariate stochastic volatility. Granger (1969, 1980) determines the causal relationship between the variables, but does not consider sunch relationship between the variables’ volatility. Yu and Meyer (2006) summarize the typified characteristics of the financial variable and argue that the multivariate stochastic volatility model is suitable for portraying the financial variable’s volatility. The authors construct the multivariate stochastic volatility model with Granger effect in volatility and the multivariate stochastic volatility model with dynamic volatility correlation coefficient. Zhang et al. (2021) empirically tests oil and stock markets’ volatility using the DGC-MSV-t Model. In addition, there is extensive research on price fluctuation synchronization. Ruan et al. (2021) examine the stock price volatility synchronization of different companies and the market, and the influence of the synchronization on information dealing efficiency. Cui et al. (2021) investigates volatilities of natural resources commodity prices and economic growth and their correlations. Zhang, Ding et al. (2022) examine the relationship of absorptivities of stock price indexes in different countries using spillover network and Granger causality test. Zhang, Yang et al. (2022) examines risk spillover effects among different commodity markets in different market conditions based on the network topology approach. Ma et al. (2022) empirically investigates the relationship between natural resources tax volatility and economic performance.