arXiv 16 Jan 2026 · Econometrics
arXiv:2601.11237 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hamilton, James D (1994) Time Series Analysis | 0.874 | 7 | 2 | 100% |
| 2 | G. E. P. Box and D. R. Cox (1964) An Analysis of Transformations | 0.811 | 4 | 2 | 100% |
| 3 | McCracken, Michael and Ng, Serena (2020) FRED-QD: A Quarterly Database for Macroeconomic Research | 0.693 | 5 | 1 | 100% |
| 4 | Hyndman, Rob J. and Athanasopoulos, G (2018) Forecasting: Principles and Practice | 0.644 | 2 | 2 | 100% |
| 5 | Peters, O. and Klein, W (2013) Ergodicity Breaking in Geometric Brownian Motion | 0.511 | 2 | 1 | 100% |
| 6 | Xiao, Han and Wu, Wei Biao (2012) Covariance Matrix Estimation for Stationary Time Series | 0.511 | 2 | 1 | 100% |
| 7 | Bańbura, Marta and Modugno, Michele (2012) Maximum Likelihood Estimation of Factor Models on Datasets with Arbitrary Pattern of Missing Data | 0.405 | 1 | 1 | 100% |
| 8 | Bel, G. and Barkai, E (2005) Weak Ergodicity Breaking in the Continuous-Time Random Walk | 0.405 | 1 | 1 | 100% |
| 9 | Caporale, Guglielmo Maria and Cuñado, Juncal and Gil‐Alana, Luis A (2012) Modelling Long‐Run Trends and Cycles in Financial Time Series Data | 0.405 | 1 | 1 | 100% |
| 10 | Chapman, S. C. and Stainforth, D. A. and Watkins, N. W (2013) On Estimating Local Long-Term Climate Trends | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 28 scored citations.