This paper describes a family of seasonal and non-seasonal time series models that can be viewed as generalisations of additive and multiplicative exponential smoothing models. Their development is motivated by fast-growing, volatile time series, and facilitated by state-of-the-art Bayesian fitting techniques. When applied to the M3 competition data set, they outperform the best algorithms in the competition as well as other benchmarks, thus achieving to the best of our knowledge the best results of univariate methods on this dataset in the literature.

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