Identifying factors that contribute to microbial growth is important for realizing efficient production of useful substrates. Our objective was to predict unknown metabolic pathways from experimental time-series data in model organisms such as Escherichia coli. We focused on a previous method that replaces the computation of auto-regression in the Granger causality test with non-parametric multiplicative regression (NPMR) to allow inferences on noisy and nonlinear data. We then proposed a new causal inference method that creates a multi-dimensional space based on the error between the time series predicted by NPMR and the original time series. We confirmed that the inference accuracy of the proposed method outperforms that of NPMR by 50% using short time series generated by coupled logistic equations, which allows for adjustment of the strength of the causal relationship. The proposed method was applied to simulation data obtained from a kinetic model for glycolysis in E. coli and achieved 61% accuracy.