Probabilistic canonical correlation analysis forecasts, with application to tropical Pacific sea-surface temperatures

Canonical correlation analysis (CCA) is a higher-dimensional extension of univariate multiple regression that is often used to construct seasonal and other forecasts in a climatological context. Although its use is widespread, to date it has apparently been used only to produce nonprobabilistic forecasts. Here an analytic result for the prediction covariance matrix of vector CCA forecasts is presented, which is sufficient to define a full forecast probability distribution if a multivariate Gaussian distribution can reasonably be assumed for the forecast errors. The approach is illustrated by computing and verifying probabilistic seasonal forecasts for tropical Pacific sea-surface temperatures.