Has anyone tried using Fractal properties for testing?
Posted: Fri May 20, 2011 1:12 pm
Hello all,
I have seen a few interesting posts here and wanted to add some input to discussions. Now the following is a little off the wall; granted, but I was curious. A few posters have discussed Mandelbrot, and one of his key assertions is that fractals (of which markets mirror) tend to be statistically self-similar at all scales.
** edit. I should clarify. He actually said they were not self-similar at all scales,
but self-affine. Slight distinction on scaling.
That being the case, has anyone thought about using much higher sampled data (say 1 min) as a proxy for the lower frequency data (daily, etc)? I know from stylized facts, that certain higher freq. data has certain properties you wouldn't see (such as greater neg. serial correlation, for example). Also, sampling too high and asynchronously (say tick data) would seem to have far more durational differences than LF data. So that's why I mentioned minutes.
Another condition, would be that it would need to be liquid on all scales (to avoid some of the duration/gap issues).
If anyone buys into this, it might be a potential source of richer data for some instruments that might have less (ETFs for example) history available. If it seems feasible, then one might be able to scale the estimates for parameters and results upwards towards the higher time frame? Even flash crashes mirror black swans on an intraday scale (although the data is likely revised backwards). I honestly haven't done the work, but curious to get some thoughts about it.
Anyways, interested to hear any yaes or naes. Also, there is a fractal generator package in R, which allows you to set scaling parameters, which might be a better simulator for those who like synthetic data that might match markets closer.
..as an example, here is something that for all intents and purposes appears as a daily sample, but is really only yesterdays data on SPY. 1 day of intraday 1min data ~ 1 full yr of daily information.
I have seen a few interesting posts here and wanted to add some input to discussions. Now the following is a little off the wall; granted, but I was curious. A few posters have discussed Mandelbrot, and one of his key assertions is that fractals (of which markets mirror) tend to be statistically self-similar at all scales.
** edit. I should clarify. He actually said they were not self-similar at all scales,
but self-affine. Slight distinction on scaling.
That being the case, has anyone thought about using much higher sampled data (say 1 min) as a proxy for the lower frequency data (daily, etc)? I know from stylized facts, that certain higher freq. data has certain properties you wouldn't see (such as greater neg. serial correlation, for example). Also, sampling too high and asynchronously (say tick data) would seem to have far more durational differences than LF data. So that's why I mentioned minutes.
Another condition, would be that it would need to be liquid on all scales (to avoid some of the duration/gap issues).
If anyone buys into this, it might be a potential source of richer data for some instruments that might have less (ETFs for example) history available. If it seems feasible, then one might be able to scale the estimates for parameters and results upwards towards the higher time frame? Even flash crashes mirror black swans on an intraday scale (although the data is likely revised backwards). I honestly haven't done the work, but curious to get some thoughts about it.
Anyways, interested to hear any yaes or naes. Also, there is a fractal generator package in R, which allows you to set scaling parameters, which might be a better simulator for those who like synthetic data that might match markets closer.
..as an example, here is something that for all intents and purposes appears as a daily sample, but is really only yesterdays data on SPY. 1 day of intraday 1min data ~ 1 full yr of daily information.