This study proposes two fuzzy clustering algorithms based on autoregressive moving average (ARMA) model for series data. The first, referred to as Tsallis entropy-regularized fuzzy c-ARMA model (TFCARMA), is created from k-ARMA, a conventional hard clustering algorithm for series data. TFCARMA is motivated by the relationship between the two clustering algorithms for vectorial data: k-means and Tsallis entropy-regularized fuzzy c-means. The second, referred to as q-divergence-based fuzzy c-ARMA model (QFCARMA), is created from ARMA mixtures, a conventional probabilistic clustering algorithm for series data. QFCARMA is motivated by the relationship between the two clustering algorithms for vectorial data: Gaussian mixture model and q-divergence-based fuzzy c-means. Based on numerical experiments using an artificial dataset, we observed the effects of fuzzification parameters in the proposed algorithms and relationship between the proposed and conventional algorithms. Moreover, numerical experiments using seven real datasets compared the clustering accuracy among the proposed and conventional algorithms.