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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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  • $\begingroup$ GARCH should not be used as a standalone model in this context, you should start with some ARIMA type model and then GARCH on the residuals. Also give a shot to seasonal ARIMA $\endgroup$ – John Jun 29 at 14:39
  • $\begingroup$ It seems to me you are thinking this the wrong way. You should start with properties of your data. Do the data show dependence not covered by correlation? What features are important? Just throwing models at the problem and then testing ever more involved ways to combine seems so wrong to me. Two BTWs: 1) What is "non-linear correlation" supposed to mean exactly? 2) Linear algorithms on general (i.e. non-linear) features does not seem very restrictive to me. $\endgroup$ – g g Jun 30 at 6:51
  • $\begingroup$ the data is financial, multivariate for multiple assets, showing properties of non i.i.d., non normality and serial correlation. Would it be correct to expect non-linear dependencies/relationships/correlation? $\endgroup$ – develarist Jun 30 at 13:51
  • $\begingroup$ deverlarist: I think what jonat is saying is that these terms you use ( non- i.i.d, non-normality and serial correlation ) are terms that are used describing error terms AFTER a model is fit. So, looking at the data itself is not the thing to focus on ( atleast with respect to those terms ) except for possibly correlation, assuming the data is financial returns. $\endgroup$ – mark leeds Jun 30 at 18:05
  • $\begingroup$ the second guy just said to look at the datas' properties before fit. and ur wrong in saying financial data gains non i.i.d., serial correlation after a model is fit on them. these properties are the very nature of the data standalone $\endgroup$ – develarist Jun 30 at 21:41

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