On Fri, Mar 12, 2010 at 12:16 PM, Robin <robince@gmail.com> wrote:
On Fri, Mar 12, 2010 at 5:10 PM, <josef.pktd@gmail.com> wrote:
On Fri, Mar 12, 2010 at 12:01 PM, Robert Kern <robert.kern@gmail.com> wrote:
On Fri, Mar 12, 2010 at 10:46, <josef.pktd@gmail.com> wrote:
On Fri, Mar 12, 2010 at 11:32 AM, <josef.pktd@gmail.com> wrote:
From the graph, it also looks like the three observations are strongly related, so separate (univariate) modeling doesn't look like the most appropriate choice.
from looking at the graphs:
If acceleration is an independent GARCH process, then velocity would just be the integral (plus noise), isn't it?
Robin will have to confirm, but I suspect that only the position was actually measured and that he derived the velocity and acceleration from the position time series numerically.
In that case it might not be to difficult to go in reverse, from acceleration to position. From the graph, I would think that acceleration is the random input for the process. Maybe with some adjustments to correct for specification errors.
Right - I am primarily working with position - vel and acc are shown just to illustrate the features I am hoping to preserve/replicate (ie transient high acceleration events which aren't really visible in the position trace, even when blown up quite a lot). I did the differentiation with basic finite differences (diff), smoothed with a 1ms (4bin moving average) (this was the method used by others previously).
Arguably acceleration is the most important of the representations (this is part of the hypothesis we are planning to test) so I agree starting from acceleration and integrating to get the actual position to use could be a good idea.
In the mean time I have to look up a lot of the other things you mentioned before I have anything sensible to add (heteroscedastic is a new one on me and I will look up GARCH and ARCH also) .
Thanks very much for the quick and useful responses!
If you have rpy and R installed, you can try something like this on your position data, to see whether GARCH is helpful (ret is my 1d numpy.array with the time series) from rpy import r r.library('fGarch') # pure garch on mean corrected data f = r.formula('~garch(1, 1)') fit = r.garchFit(f, data = ret - ret.mean(), include_mean=False) #ARMA in mean, GARCH in variance f = r.formula('~arma(1,1) + ~garch(1, 1)') fit = r.garchFit(f, data = ret) I haven't figured out how to do many of the options for GARCH with rpy. Josef
Cheers
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