Random autoregressive models: A structured overview

TL;DR

This paper provides a comprehensive structured overview of autoregressive models with random coefficients, highlighting their properties, estimation methods, and applications in analyzing complex high-frequency time series.

Contribution

It systematically organizes the literature on these models, clarifying hierarchies, analogies, and combining strengths of various approaches.

Findings

Detailed taxonomy of models and their properties

Comparison of estimation methods and software tools

Guidance on applications in high-frequency data analysis

Abstract

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 sectorial, 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 random coefficients. We describe hierarchy and analogies among models, and for each we systematically list properties, estimation methods, tests, software packages and typical applications.