1. Specification of ARIMAX model for natural gas price and plastic price

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Supplementary information for

An energy system optimization model accounting for the interrelations of multiple stochastic energy prices Strategic and operational decision-making of energy supply chain system accounting for the

interrelations of multiple volatile energy markets

1. Specification of ARIMAX model for natural gas price and plastic price

As discussed in the main text, natural gas price and downstream plastic price are modelled by ARIMAX, in which oil price serves as the exogenous variable. The following procedure is followed to specify the model. First, differencing of order d1 is taken to achieve stationarity. Figs. S1 and S2 show the results for natural gas price and plastic product price, respectively, both withd1and

2

d . Second, autocorrelation and partial autocorrelation are obtained to determine p and q, the

results are shown in Figs. S3 and S4. These results indicate the most appropriate value of p and q are that p2 and q2 for natural gas, and p1 and q1. After p and qare determined, the distribution of residuals should be examined via Durbin Watson (DW) test (Figs. S5 and S6) to ensure that all the information has been extracted.

Fig. S1 Differencing and stationarity for natural gas price time series

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Fig. S2 Differencing and stationarity for plastic price time series

Fig. S3 Autocorrelation and partial autocorrelation for natural gas price time series

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Fig. S4 Autocorrelation and partial autocorrelation for plastic price time series

Fig. S5 Autocorrelation and partial autocorrelation

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Fig. S6 Autocorrelation and partial autocorrelation

2. Deterministic model results

Fig. S7 Operational monthly production of the three technologies in PS1

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Fig. S13 price variations of coal, natural gas and oil in the six scenarios