An important feature of the time series in the real world is that its distribution has different degrees of asymmetry, which is what we call irreversibility. In this paper, we propose a new method named permutation pattern (PP) to calculate the Kullback–Leibler divergence ( $${D}_{\mathrm{KL}}$$ D KL ) and the Jensen–Shannon divergence ( $${D}_{\mathrm{JS}}$$ D JS ) to explore the irreversibility of time series. Meanwhile, we improve $${D}_{\mathrm{JS}}$$ D JS and obtain a complete mean divergence ( $${D}_{\mathrm{m}}$$ D m ) through averaging $${D}_{\mathrm{KL}}$$ D KL of a time series and its inverse time series. The variation trend of $${D}_{\mathrm{m}}$$ D m is similar to $${D}_{\mathrm{JS}}$$ D JS , but the value of $${D}_{\mathrm{m}}$$ D m is slightly larger and the description of irreversibility is more intuitive. Furthermore, we compare $${D}_{\mathrm{JS}}$$ D JS and $${D}_{\mathrm{m}}$$ D m calculated by PP with those calculated by the horizontal visibility graph, and discuss their respective characteristics. Then, we investigate the advantages of $$\mathrm{D}_{\mathrm{JS}}$$ D JS and $${D}_{\mathrm{m}}$$ D m through length variation, dynamic time variation, multiscale and so on. It is worth mentioning that we introduce Score and variance to analyze the practical significance of stock irreversibility.