fractional differencing parameter improves with denoising by wavelet thresholding for 3000 stocks
June 11, 2015 by zulfahmed
This is a previous result of mine on actual data: fractional differencing parameter, for ARFIMA models which are stochastic, but they do give us an estimate of the correct fractional order. I will redo this exercise in the next days with new data and clearer sense of what we’re looking for: a fractional differential equation on a complex network with white noise.
These tell us that we have better than Holder continuity closer to C^(0.3-0.4) or so under the data for individual stock volatility which is now a rough collective measure just from the actual differencing figures in the link above. This suggests that what should be the focus are fractional partial differential on complex networks. So now we can return to the Wolfe graph models and consider fractional equations on complex networks that are not scale-free in degree distributions. We still want to consider equations
((d/dt)^(alpha) – Laplacian)u = F(u)
Now we want to set alpha as a function of the estimated Hurst parameter from a model assuming fractional dynamics where wavelet denoising provides theory guaranteed to recover the Besov signals which are solutions of these equations. This is a good understanding because we are using known non-Markov information about volatility. So if we go this route we do have a path back to Onsager’s analysis of creation of vortex bubbles possibly.
Ok this is a good direction. Thanks!!