Model-based maximum covariance analysis for irregularly observed climatological data

In climatology, maximum covariance analysis (MCA) is one of the most popular tools for investigating association between two multivariate variables across time and space. These association studies are important because many climate phenomena such as the El Niño-Southern Oscillation (ENSO) and the North Atlantic Oscillation are results of interaction between these variables. Despite its popularity, maximum covariance analysis does not provide straightforward statistical inference on its estimates and furthermore it does not provide an objective way to handle irregularly observed data, frequently encountered in climatology. The aim of this article is to describe a model-based maximum covariance analysis that can accommodate irregularly observed data. The methodology combines maximum covariance analysis's relationship with Tucker inter-battery factor analysis and the state-space methodology for missing data. The methodology is illustrated with an application to investigate association between Irish winter precipitation and global sea surface temperature (SST) anomalies.