arXiv 15 Sep 2026 · Statistics — Applications
arXiv:2609.16509 · PDF · Extracted main text
Anthropogenic forcing components follow different long-run paths, while persistent temperature change can involve distributional changes beyond the mean. Scalar regressions aggregate these components and retain only mean temperature, obscuring how distinct forcing paths relate to persistent distributional change. We develop new testing, estimation, and inference methods for long-run relations between an integrated predictor vector and a density-valued response. These comprise a residual-based test of between-cointegration (whether predictor trends account for all stochastic trends in the response density), a fully modified least-squares estimator of predictor-specific functional responses, and simulation-based inference for interpretable projections. We apply the methods to densities of observed local temperature anomalies and anthropogenic effective radiative forcing divided into CO$_2$ and non-CO$_2$ portfolios. The test results are consistent with persistent movements in these portfolios statistically accounting for the persistent evolution of the anomaly distribution, with no additional stochastic trend detected in the residual. A joint test rejects the common-response restriction imposed by aggregating the two portfolios. The fitted CO$_2$ response mainly shifts mass toward warmer anomalies and increases central concentration, whereas the non-CO$_2$ response produces a smaller shift but greater dispersion and off-center reshaping. Positive fitted mean responses for both portfolios conceal these contrasts, demonstrating the information lost through scalar aggregation.
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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 | Nam \ Seo (2025) `Functional regression with nonstationarity and error contamination: Application to the economic impact of climate change', arXi… | 0.843 | 4 | 4 | 75% |
| 2 | Chang, Kaufmann, Kim, Miller, Park \ Park (2020) `Evaluating trends in time series of distributions: A spatial fingerprint of human effects on climate', Journal of Econometrics… | 0.843 | 4 | 4 | 75% |
| 3 | Phillips (1995) `Fully modified least squares and vector autoregression', Econometrica 63(5), 1023–1078 | 0.737 | 5 | 3 | 40% |
| 4 | Beare, Seo \ Seo (2017) `Cointegrated linear processes in Hilbert space', Journal of Time Series Analysis 38(6), 1010–1027 | 0.737 | 3 | 3 | 67% |
| 5 | Chang, Kim \ Park (2016) `Nonstationarity in time series of state densities', Journal of Econometrics 192(1), 152 – 167 | 0.737 | 3 | 3 | 67% |
| 6 | Seong \ Seo (2025) `Functional instrumental variable regression with an application to estimating the impact of immigration on native wages', Econo… | 0.737 | 3 | 3 | 67% |
| 7 | Morice, Kennedy, Rayner, Winn, Hogan, Killick, Dunn, Osborn, Jones \… (2021) `An updated assessment of near-surface temperature change from 1850: The HadCRUT5 data set', Journal of Geophysical Research: At… | 0.644 | 3 | 2 | 67% |
| 8 | Egozcue, Díaz-Barrero \ Pawlowsky-Glahn (2006) `Hilbert space of probability density functions based on Aitchison geometry', Acta Mathematica Sinica 22(4), 1175–1182 | 0.644 | 2 | 2 | 100% |
| 9 | IPCC (2021) Annex iii: Tables of historical and projected well-mixed greenhouse gas mixing ratios and effective radiative forcing of all cli… | 0.644 | 2 | 2 | 100% |
| 10 | Nielsen, Seo \ Seong (2023) `Inference on the dimension of the nonstationary subspace in functional time series', Econometric Theory 39(3), 443–480 | 0.644 | 2 | 2 | 100% |
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