arXiv 26 Feb 2026 · Econometrics
arXiv:2602.23482 · PDF · DOI · OpenAlex · Extracted main text
This paper develops inference methods for ratios of deterministic trend slopes in systems of pairs of time series. Hypotheses based on linear cross-equation restrictions are considered with particular interest in tests that trend ratios are equal across pairs of trending series. Tests of equal ratios can be used for the empirical assessment of climate models through comparisons of trend ratios (amplification ratios) of model generated temperature series and observed temperature series. The analysis in this paper builds on the estimation and inference methods developed by Vogelsang and Nawaz (2017, Journal of Time Series Analysis) for a single pair of trending time series. Because estimators of ratios can have poor finite sample properties when the trend slope are small relative to variation around the trends, tests of equal trend ratios are restated in terms of products of trend slopes leading to inference that is less affected by small trend slopes. Asymptotic theory is developed that can be used to generate critical values. For tests of equal trend ratios, finite sample performance is assessed using simulations. Practical advice is provided for empirical practitioners. An empirical application compares amplification ratios (trend ratios) across a set of five groups of observed global temperature series.
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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 | Vogelsang and Nawaz (2017) Estimation and inference of linear trend slope ratios with an application to global temperature data, Journal of Time Series Ana… | 1.000 | 14 | 6 | 100% |
| 2 | Bunzel and Vogelsang (2005) Powerful trend function tests that are robust to strong serial correlation with an application to the prebisch-singer hypothesis… | 0.874 | 6 | 2 | 100% |
| 3 | Kiefer and Vogelsang (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests, Econometric Theory 21, 1130–1164 | 0.843 | 4 | 3 | 75% |
| 4 | Fieller (1954) Some problems in interval estimation, Journal of the Royal Statistical Society Series B: Statistical Methodology 16(2), 175–185 | 0.644 | 2 | 2 | 100% |
| 5 | Lazarus, Lewis and Stock (2021) The size-power tradeoff in HAR inference, Econometrica 89(5), 2497–2516 | 0.405 | 1 | 1 | 100% |
| 6 | Lazarus, Lewis, Stock and Watson (2018) HAR inference: Recommendations for practice, Journal of Business & Economic Statistics 36(4), 541–559 | 0.405 | 1 | 1 | 100% |
| 7 | Vogelsang, McKitrick, Christy and Spencer (2026) Biased trend amplification ratios in CMIP6 models | 0.405 | 1 | 1 | 100% |
| 8 | Andrews (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation, Econometrica 59, 817–854 | 0.405 | 1 | 1 | 100% |
| 9 | Christy, Herman, Pielke Sr., Klotzbach, McNider, Hnilo, Spencer, Cha… (2010) What do observational datasets say about modeled tropospheric temperature trends since 1979?, Remote Sensing 2(9), 2148–2169 | 0.405 | 1 | 1 | 100% |
| 10 | Jansson (2004) The error rejection probability of simple autocorrelation robust tests, Econometrica 72, 937–946 | 0.405 | 1 | 1 | 100% |
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