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Likelihood-Based Ergodicity Transformations in Time Series Analysis

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  • Anthony Britto

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.

Suggested Citation

  • Anthony Britto, 2026. "Likelihood-Based Ergodicity Transformations in Time Series Analysis," Papers 2601.11237, arXiv.org.
    • Handle: RePEc:arx:papers:2601.11237
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    File URL: http://arxiv.org/pdf/2601.11237
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