Abstract
Adapting to human-induced climate change is becoming an increasingly important aspect of sustainable development. To be able to do this effectively, it is important to know how much human influence has contributed to observed climate trends. Climate detection and attribution (D&A) studies achieve this by estimating scaling factors usually obtained by performing a least squares regression of the observed trending climate variable on the equivalent variable simulated by a climate model. This study proposed instead to estimate scaling factors by using the econometric approach of dynamically modelling the time series as a cointegrating Vector Auto-Regressive (VAR) time series process. It is shown that a 2nd-order cointegrating VAR(2) model is theoretically justified if the observed and simulated variables can be represented as a one-box AR(1) response to a common integrated forcing. The VAR(2) model can be expressed as a Vector Error-Correction Model (VECM) and then fitted to the data to obtain the cointegration relationship, the stationary linear combination of the two variables, from which the scaling factor is then easily obtained. Estimates of the scaling factor from the VAR(2) model are critically compared to those from Ordinary Least Squares (OLS) and Total Least Squares (TLS) for annual Global Mean Surface Temperature (GMST) data simulated by a simple stochastic model of the carbon–climate system and for historical simulations from 16 climate models in the Coupled Model Intercomparison Project 5 (CMIP5) experiment. Results from the toy model simulations show that the slope estimates from OLS are negatively biased, TLS estimates are less biased but have high variance, and the VAR(2) estimates are unbiased and have lower variance and provide the most accurate estimates with smallest mean squared error. Similar behaviour is noted in the CMIP5 data. Hypothesis tests on the VAR(2) fits found strong evidence of a cointegrating relationship with the observations for all the CMIP5 simulations.