Likelihood-Based Ergodicity Transformations in Time Series Analysis

TL;DR

This paper introduces a likelihood-based method for estimating ergodicity transformations in time series, improving forecasting and inference for non-ergodic data across various models.

Contribution

It presents a broadly compatible approach for estimating ergodicity transformations, demonstrated through simulations and macroeconomic data case studies.

Findings

Successfully recovers known ergodicity transformations in simulations

Improves model performance in macroeconomic data analysis

Compatible with Gaussian, ARMA, GARCH models

Abstract

Time series often exhibit non-ergodic behaviour that complicates forecasting and inference. This article proposes a likelihood-based approach for estimating ergodicity transformations that addresses such challenges. The method is broadly compatible with standard models, including Gaussian processes, ARMA, and GARCH. A detailed simulation study using geometric and arithmetic Brownian motion demonstrates the ability of the approach to recover known ergodicity transformations. A further case study on the large macroeconomic database FRED-QD shows that incorporating ergodicity transformations can provide meaningful improvements over conventional transformations or naive specifications in applied work.