Dear Astor,
thanks for answering. I needed a bit of time, to have a closer look.
Here is my answer.
Regarding
> firstDerivative = velocity = priceChange / timeChange = (EMA(5) - EMA(60)) /
> (1 hr) = (110 - 100) / (1 hr) = 10.
yes. This makes sense. However, the firstderivative has an unclear
relation (depending on 5 and 60) to the
"true" first derivative of the "real" time series. - This is exactly
the point puzzling me, here.
Thanks also for the paper. I read it. It looks very convincing at
first sight, but then I could not answer the following
question based on it. How did the author determine the two parameters
in the double exponential for his values.
His claims are:
- it is faster; no problems here
- it is nearly as accurate?
might be, for some parameters. But this is exactly the optimization
problem: it might be possible to find
optimized values that yield the results, but it would be invalid to
simply assume the result would also work
on data that did not participate in the optimization.
Unfortunately, the author does not say anything about this.
Additionally, even the author does not claim that he would approximate
the first derivative..
Cheers
Klaus
On May 11, 11:33 pm, Astor <[email protected]> wrote:
> If you are looking for a bit of mathematical theory on this type of
> methodology, take a look at the attached pdf.
> From: nonlinear <[email protected]>
> To: [email protected]
> Sent: Wednesday, May 11, 2011 4:08 PM
> Subject: [JBookTrader] Re: Book trading discussion
>
> On Wednesday, May 11, 2011 1:05:41 PM UTC-4, Klaus wrote:
>
> now I am puzzled. Why would you do this?
>
> >The first derivative is the change rate. Ok, I would understand one
> >does want to do some
> >smoothing. But the difference between short and longterm EMA certainly
> >isn't the first derivative.
> >It does not seem to be a very good approximation, either.
>
> >I can see this is a somewhat bizarre change rate indicator, though.
> >And it might have some merits, if it just works..
>
> Well, I disagree that it a "bizarre" indicator. Consider MACD, a well
> researched and very popular indicator. The MACD signal line is defined as the
> difference between the shorter and longer term EMAs, which is precisely what
> the PriceVelocity indicator in JBT does. The BalanceVelocity indicator in JBT
> also uses the same concept, applied to book balances. The Tension indicator
> in JBT is the difference between BalanceVelocity and PriceVelocity.
>
> In regards to whether the difference between the shorter and longer term EMAs
> is a good approximation of velocity (i.e. the first derivative of a given
> quantity with respect to time) is debatable. If you can think of better ways
> of calculating the first derivative from a notoriously noisy time series,
> please let me know, and we can certainly experiment with it. However,
> intuitively, it makes sense to me the way it is right now. Think of it this
> way: if the average price over the last 5-minute interval was 110 and the
> average price over the last 60-minute interval was 100, then the first
> derivative is:
>
> firstDerivative = velocity = priceChange / timeChange = (EMA(5) - EMA(60)) /
> (1 hr) = (110 - 100) / (1 hr) = 10.
> Does this make sense?
>
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> double exponential regression.pdf
> 49KViewDownload
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