Linear Correlation Limits in Volatility Forecast Combination

Summary

The document questions whether linear correlation is sufficient when studying relationships among financial variables and combining volatility forecasts. It describes a proposed comparison of GARCH, support vector regression, and fractionally differenced ARIMA forecasts, each trained on the same data and evaluated over the same test period. The author asks whether their prediction errors or forecast vectors might be related nonlinearly, and whether ordinary correlation would then be misleading.

The text offers no answer, results, or recommended information-theoretic distance measure. It is best read as a research question rather than an established claim that financial relationships or model outputs are generally nonlinear. It does not specify a forecast-combination method, validation design, or how to separate dependence in forecast levels from dependence in forecast errors. Those distinctions matter when assessing whether models contribute complementary information and when selecting dependence measures.

Key ideas

• The document asks whether linear correlation captures dependence among financial predictors and volatility forecasts adequately.
• It proposes comparing forecasts from GARCH, support vector regression, and fractionally differenced ARIMA on shared data.
• It raises nonlinear dependence as a possibility but provides no evidence that the forecasts exhibit it.
• The note asks about alternative distance measures but recommends none.

Tags

# Is non-linear correlation problematic in financial time series prediction?


# Is non-linear correlation problematic in financial time series prediction?












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)?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.