[SciPy-User] OT: advice on modelling a time series

[Robin]

On Fri, Mar 12, 2010 at 5:10 PM,  <josef.pktd at gmail.com> wrote:
> On Fri, Mar 12, 2010 at 12:01 PM, Robert Kern <robert.kern at gmail.com> wrote:
>> On Fri, Mar 12, 2010 at 10:46,  <josef.pktd at gmail.com> wrote:
>>> On Fri, Mar 12, 2010 at 11:32 AM,  <josef.pktd at 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!

Cheers

Robin