Many traditional finance models assume linear relationships between variables and features. Aren't linear correlations/covariances unable to capture financial processes empirically since they actually are more likely to possess non-linear correlations?
If I am trying to forecast volatility with 3 different algorithms, for example, GARCH, Support Vector Regression (SVR) and fractionally-differenced ARIMA (ARFIMA), using the same training data for the 3 models to predict the same test data, and want to combine them somehow to build upon their individual strengths, should I expect that these 3 prediction vectors will be correlated non-linearly, not linearly?
If so, why. Would the traditional correlation measure be unreliable, given that it assumes linear relationships, causing the need instead for distance metrics from information theory (any examples recommended for finance)?