Random autoregressive models: A structured overview

Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sector-specific, overlapping, and confusing. Most models focus on one property of the data, while much can be gained by combining the strength of various models and their sources of heterogeneity. We present a structured overview of the literature on autoregressive models with ran- dom coefficients. We describe hierarchy and analogies among models, and for each we systematically list properties, estimation methods, tests, soft- ware packages and typical applications.