对系统方程中线性趋势斜率比的假设检验：以检验各对趋势系列中趋势比相等的检验为重点
Testing Hypotheses About Ratios of Linear Trend Slopes in Systems of Equations with a Focus on Tests of Equal Trend Ratios
AI总结：
本文提出了一种检验系统方程中趋势比相等的方法，通过重新表述为趋势斜率乘积以提高有限样本性能，并应用于气候模型的实证分析。
摘要：
本文开发了用于系统中成对时间序列确定性趋势斜率比的推断方法。考虑了基于线性跨方程限制的假设，特别关注检验各对趋势系列中趋势比是否相等的检验。检验趋势比相等可以用于通过比较模型生成的温度系列和观测温度系列的趋势比（放大比）来评估气候模型。本文的分析建立在Vogelsang和Nawaz（2017，时间序列分析杂志）为单对趋势时间序列开发的估计和推断方法的基础上。由于趋势斜率比的估计在趋势斜率相对于趋势周围变化较小时可能具有较差的有限样本性质，因此将趋势比相等的检验重新表述为趋势斜率乘积，从而得到受小趋势斜率影响较小的推断方法。开发了可用于生成临界值的渐近理论。对于趋势比相等的检验，通过模拟评估有限样本性能。为经验研究者提供了实用建议。一个实证应用比较了五组观测全球温度系列中的放大比（趋势比）。
英文摘要：
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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