Sparse pre-whitening operators for regression of climatic time series

Regression methods are used extensively in climate science and are commonly applied to output from numerical climate models, e.g. for detection and attribution of climate change trends and for diagnosing emergent properties of climate models such as Equilibrium Climate Sensitivity (ECS). Output from climate models can have complex spatiotemporal dependence structures and, in practice, the assumptions of the Gauss-Markov Theorem seldom hold. Under such conditions, the application of Ordinary Least Squares (OLS) is inefficient and can lead to biased inference, with implications for model selection and evaluation.

The detection and attribution community has traditionally addressed this problem using a Generalised Least Squares (GLS) approach, whereby a pre-whitening operator is estimated from a climate model's pre-industrial control (piControl) simulation, typically using an unstructured sample covariance matrix or regularised version thereof.

We show how, for low-dimensional collections of climate variables, the dependence structure can be parsimoniously parameterised as a Vector AutoRegression (VAR) and the resultant sparse pre-whitening operator efficiently computed. For the first-order VAR(1) model, this procedure is analogous to a multivariate Prais-Winsten estimation. An example application to calibration of Simple Climate Models (SCMs) is discussed, shedding new light on the problem of choosing an appropriate model complexity.