Sequential tests of causality between environmental time series: With application to the global warming theory

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.