(This article was originally published at No Hesitations, and syndicated at StatsBlogs.)

But the popular volatility models are effectively linear (ARMA) in squares. Maybe that's too rigidly constrained. Volatility dynamics seem like something that could be nonlinear in ways much richer than just ARMA in squares.

Here's an attempt using deep neural nets. I'm not convinced by the paper -- much more thorough analysis and results are required than the 22 numbers reported in the "GARCH" and "stocvol" columns of its Table 1 -- but I'm intrigued.

It's quite striking that neural nets, which have been absolutely transformative in other areas of predictive modeling, have thus far contributed so little in economic / financial contexts. Maybe the "deep" versions will change that, at least for volatility modeling. Or maybe not.

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