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In this study, we explore the subtle temporal structure of environmental data using symbolic information-theory approach. The newly developed multivariate multiscale permutation entropy and complexity-entropy causality plane methodology are applied to the six pollutants data recorded in Beijing during 2013–2016, which is a powerful tool to discriminate nonlinear deterministic and stochastic dynamics. The obtained results showed that pollutant series exhibit significant randomness and a lower level of predictability in spring and summer, and more temporal correlations in winter and fall. In addition, surrogate analysis is implemented to avoid biased conclusion. We also define the relative complexity measure of multivariate series to reflect the complexity of a system. The highest relative complexity in winter is in line with the physical behavior of the pollution phenomenon. [ABSTRACT FROM AUTHOR]