This article proposes the generalized discrete autoregressive moving‐average (GDARMA) model as a parsimonious and universally applicable approach for stationary univariate or multivariate time series. The GDARMA model can be applied to any type of quantitative time series. It allows to compute moment properties in a unique way, and it exhibits the autocorrelation structure of the traditional ARMA model. This great flexibility is obtained by using data‐specific variation operators, which is illustrated for the most common types of time series data, such as counts, integers, reals, and compositional data. The practical potential of the GDARMA approach is demonstrated by considering a time series of integers regarding votes for a change of the interest rate, and a time series of compositional data regarding television market shares.

中文翻译：

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广义离散自回归移动平均模型

本文提出了广义离散自回归移动平均（GDARMA）模型，将其作为平稳的单变量或多元时间序列的一种简约且普遍适用的方法。GDARMA模型可以应用于任何类型的定量时间序列。它允许以独特的方式计算力矩特性，并且展现了传统ARMA模型的自相关结构。通过使用特定于数据的变化运算符可以获得极大的灵活性，该运算符可用于最常见的时间序列数据类型，例如计数，整数，实数和成分数据。通过考虑与利率变化有关的投票的整数时间序列以及与电视市场份额有关的成分数据的时间序列，可以证明GDARMA方法的实际潜力。