Analysis of the causality between environmental time series is particularly debated nowadays. Checking if the global warming is caused by human activities or the solar irradiance, or if air pollution is produced by industrial plants or consumers' behavior are typical examples. Statistical methods for testing these hypotheses mainly focus on bivariate autoregressive (ARX) models and their fitting performance; in particular, the Granger test uses classical F‐statistics. In this article, we discuss a further measure based on the sum of dynamic multipliers which enables to capture the total forcing (gain) of a series on another. We consider its statistical distribution in the case of time series with trends and cycles and we adapt the methodology to the case of models with time‐varying parameters. In particular, the recursive least squares (RLS) algorithm with exponentially weighted (EW) observations is used to estimate parameter changes. The approach is fundamentally semiparametric in that the observable model is linear but its parameters change in an unknown manner. Furthermore, EW‐RLS is a smoother whose bandwidth can be selected with cross‐validation techniques. An extensive application to both global annual and local monthly time series shows significant evidence of the causality CO₂‐temperature; in particular, the beginning of the forcing started during the second world war and was relatively fast and permanent.

中文翻译：

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环境时间序列之间因果关系的顺序检验：在全球变暖理论中的应用

如今，有关环境时间序列之间因果关系的分析尤其受到争议。典型的例子是检查全球变暖是由人类活动或太阳辐射引起的，还是由工厂造成的空气污染或消费者的行为。用于检验这些假设的统计方法主要集中于双变量自回归（ARX）模型及其拟合性能。特别是Granger检验使用经典F-统计。在本文中，我们将讨论基于动态乘数之和的另一种度量，该度量能够捕获另一个序列的总强迫（增益）。我们在具有趋势和周期的时间序列的情况下考虑其统计分布，并且使该方法适用于具有时变参数的模型的情况。特别地，具有指数加权（EW）观测值的递归最小二乘（RLS）算法用于估计参数变化。该方法基本上是半参数的，因为可观察模型是线性的，但是其参数以未知的方式改变。此外，EW‐RLS更平滑，其带宽可以使用交叉验证技术进行选择。广泛应用于全球年度和本地每月时间序列显示了因果关系的重要证据_2-温度; 特别是，强迫的开始是在第二次世界大战期间开始的，相对较快和持久。