## 2 Literature Review  
The impact of crude oil price fluctuation on inflation and GDP has always been an important issue [15; 16; 17; 18]. The price indices are widely used to represent inflation. According to the research aims, the related existing studies can be divided into the following three categories. First, the heterogeneous impacts of crude oil price fluctuations on inflation in different economies have been proved [19; 20; 21]. Researchers revealed that oil market volatility strongly and negatively affects real economic growth. Specifically, it exerts more pressure on inflation in Saudi Arabia and the United Kingdom [22; 23] but less influence on the ASEAN-5 economies (Thailand, Malaysia, Singapore, the Philippines, and Indonesia) in the long run [24]. Oil price could exert a more significant impact on inflation of net oil-importing countries than their oil-exporting counterparts in the long run [25]. [PERSON], [PERSON] et al. studied the effects of international oil price fluctuations on the inflation of 72 advanced and developing economies and found that a 10% increase in crude oil price could cause domestic inflation by increasing approximately 0.4% on average, with the influence vanishing after two years [26]. They explained that the share of transport in the CPI basket and energy subsidies are the most robust factors in explaining cross-country variations in the effects of oil price shocks. As for China, a net importer of crude oil, crude oil price fluctuations are more likely to influence its inflation significantly [18; 19]. The pass-through effects of global oil price on China's producer prices index (PPI) and consumer prices index (CPI)have been demonstrated [2], and demand shocks that are specific to the crude oil market contribute the most to the fluctuations in China's inflation [27; 28]. Second, the non-linear effects of oil price on inflation have been revealed based on nonlinear ARDL methods [9; 29], the Markov Regime Switching Vector Autoregressive model [30], and non-linear causality tests [31]. [PERSON] and [PERSON] [32] proved the nonlinear impacts of oil price on inflation in Algeria. Specifically, there is a significant relationship between the rise in oil price and inflation rate. However, there is no significant relationship between the decline in oil prices and inflation. [PERSON] and [PERSON] [2] studied the pass-through effects of international crude oil price on China's CPI and PPI and found that the long-term impacts of the oil price reduction on China's inflation are lower than the oil price increases on inflation. However, researchers found that the impacts on African OPEC member countries' inflation were found to be more significant when the oil prices decreased [33]. Third, the impacts of oil price fluctuations on various price indices are also different [5; 34; 35]. For example, in Malaysia, oil price changes could directly cause higher import and production prices through cost channels but have a limited direct effect on consumer prices [29]. Researchers also revealed that an increase in oil price had a stronger effect on the PPI than the CPI in Indonesia and Thailand [36]. Similar effects of oil price shocks on CPI and PPI in China were also proven, i.e., the demand shocks of oil price had significant effects on China's PPI, while the impacts failed to be transmitted to China's CPI [28]. The above literature mainly focuses on the transmission mechanism from oil price fluctuation to CPI or PPI using econometric models from a macro perspective. However, other macro price indices could also represent the price level of an economy to a certain degree, such as the retail price index (RPI), the purchasing price index of raw material, fuel, and power (PPIRM), and so on. More importantly, there are complex links between these price indices. Previous studies ignored the transmission relationships between crude oil and other price indices, such as RPI and PPIRM.