Re: Taylor approximation of unknown function

Adam Chapman wrote:
I read at http://www.forexfactory.com/showthread.php?t=68181 ;


"Looks to me like a simple raised-cosine-windowed root-nyquist filter
with the coeffs tweaked by the trusty old Remez Exchange algorithm.
Should take around 10 minutes on MatLab to knock up something
equivalent or better..."

Now I understand the raised cosine as a "Hamming Window". My
understanding of this is also that your target sample should be in the
middle of that window, i.e. you need to have data in the widnow before
and AFTER the point you are analysing, which is useless in trading.

If you center the window on the current time point(if exactly real time) then the filter cannot be real time. It requires you introduce a delay so that you can get enough data points. The filter without the delay is non-causal. With the delay it is causal and can be implemented in "real time". It is only quasi real time as you actually have a delay between the input and output. Generally the delay is insignificant compared in the time it is used.

Unless you are doing it in a frequency domain.

Could you please explain the meaning of non-causality in an algorithm?
UI understand what the term non-causal means but no real bearing on
how it applies here.

A non-causal algorithm is one that cannot be implemented in real time because it requires future events. Take a simple missile tracking system. The tracking cannot use future events because they haven't happened yet(it could use some predictive scheme though). It would be very bad for the algorithm to have a "lag" because this means that what is actually happening does not correspond to what the algorithm belives to be happening. i.e., the missle will almost always miss(although some lag is acceptable).

Basically the further into the future you need to look for the algorithm to work is equivalent to shifting the output of the algorithm back in time(since you can't really look into the future). This creates a time delay between the algorithm and the actual event. The delay maybe acceptable but in real time systems the delay is generally not. One also has an inherent lag created by the computational complexity.

An example is your stock trading. It would do you no good if it takes months to compute a trend as the time you learned that the trend would have changed. Similarly if the algorithm was non-causal it would introduce a lag(because it has to actually wait for the future to arrive) which may be unacceptable.

.

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