Non-Gaussian ARMA models are used to analyze sequences of random numbers. These models are different from traditional Gaussian models and can represent various types of distributions. They share similarities with linear models in terms of predicting future values and how correlations change over time. The variance of observations can depend on past values. Estimation methods vary depending on the distribution type, with some cases allowing for straightforward maximum likelihood estimation. Mixing properties are used to understand how well the estimators work in practice.