Stochastic Equicontinuity in Nonlinear Time Series Models

TL;DR

This paper establishes simple, verifiable conditions for stochastic equicontinuity in various nonlinear time series models, avoiding mixing conditions, and discusses multiple applications.

Contribution

It introduces a novel approach to stochastic equicontinuity that bypasses mixing conditions, applicable to a broad class of modern nonlinear time series models.

Findings

Provides verifiable conditions for stochastic equicontinuity

Avoids reliance on mixing conditions in proofs

Demonstrates applications in multiple time series models

Abstract

In this paper I provide simple and easily verifiable conditions under which a strong form of stochastic equicontinuity holds in a wide variety of modern time series models. In contrast to most results currently available in the literature, my methods avoid mixing conditions. I discuss several applications in detail.