Calculus- Useful in Systems?

Quote from stephencrowley:

Of course, autocorrelation is all about lags.. but calculus is very useful in the calculation and prediction of volatility, which is very useful for risk analysis, and also helps predict the SIZE of that SIGN change.
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Steve, I think your talking to an add/delete guy.....

It appears that we ganged up on him with the rate of change of change stuff.
 
So your saying I am on the right road, which means my intuition is correct. I read about and was warned that linear systems dont work when trading, so I guess I need to learn this advanced calculus, non-continuous, etc.... I'll see how it goes.

See you in 3 years.
 
Good old Jack. Talking about second derivatives shows he hasn't actually tried to CALCULATE one on real-time data. It's INTEGRALS that are useful.
 
Quote from Grob109:


Calculus (in the form of stats for non continuous functions) is THE PATH to take in the fork in the road leading to very high money velocity trading profits.
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Hey,
I always thought all you needed for that was Jack's tricks.

:D
 
Quote from Grob109:

.....

Calculus starts the ball rolling when you go from conventional indicator signals to the appropriate signal sets which are leaders in terms of price. Then you are on the trail of inflection points in periodic functions that derive out of the indicators.

....
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OK. Well, the implication of this statement is that you have the situation all wrapped up and that the magical world of mathematics is that holy grail. The problem is that many markets behave in all sorts of ways: they dont fit neatly into any particular analysis. Yes, periodic functions (think Sin, Sinh etc) have a lot of utility but just like any type of signal processing you can often need a LOT of sampling to determine if anything is actual signal - and not noise - and then, often by the time you identify a signal, it has gone away.

This is all a longwinded way of saying that you will perhaps find these methods useful, but at the end of the day you will need to construct your own indicator and trading strategy based upon your understanding of the how markets are actually traded (in addition to other factors) and this information can not really be provided by any magical formula.....

... or I could have just said that constructing profitable trading strategies (and executing them) is hard ....
 
It's useful, but you should keep it on the simple side, IMHO. For example here is a small part of my daytrade scalper program. Something like this is all you really need:

<P>
(1) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img66.gif">, iff <i>V</i>(<i>x</i>) is an arbitrary
differentiable function;
<P>
(2) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img67.gif">, iff <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img68.gif">;
<P>
(3) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img69.gif">, iff
<IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img70.gif"> the following equalities are true:
<P><IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img71.gif"><P>
<P>
(4) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img72.gif">, iff <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img73.gif">,
<IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img74.gif"> are constants and (9) are true. <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img75.gif">
are the binomial coefficients.
<P>
The operators in theorem 3 have the following representation:
<P><IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img76.gif"><P>
<i>I</i> is the unit operator.
<P>
<i> Consequence</i>. The 2<i>n</i>th-order PDE
<P><IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img77.gif"><P>
is invariant under the following algebras:
<P>
(1) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img78.gif">, iff <i>V</i>(<i>x</i>) is an arbitrary
differentiable function;
<P>
(2) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img79.gif">, iff <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img80.gif">;
<P>
(3) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img81.gif">, iff <i>V</i> = 0;
<P>
(4) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img82.gif">, iff <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img83.gif"> where <i>C</i> is an
arbitrary constant.
<P>
The above operators have representation (10) with
<IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img84.gif">.
<P>
Note that symmetry classification of potentials for the
fourth-order PDE of the form
<P><IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img85.gif"><P>
was carried out in [<A HREF="#Sym">8</A>]. In this case, symmetry operators
have representation (10) with <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img86.gif"> and <i>n</i> = 2.
<P>
(iii) Now, let us consider nonlinear PDEs of type (4)
in (<i>r</i> + 1)-dimensional space:
<P><IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img87.gif"><P>
where <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img88.gif"> is complex conjugated function, <i> n </i> is an
arbitrary integer power and <i>F</i> is an arbitrary complex function
of <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img89.gif">
<P>
We study symmetry classification of (11), i.e. we find
all functions <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img90.gif"> which admit an extension of
symmetry of equation (11).
<P>
<i> Theorem 4</i>
Equation (11) is invariant under the following algebras:
<P>
(1) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img91.gif">, iff <i>F</i> is an
arbitrary differentiable function;
<P>
(2) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img92.gif">, iff <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img93.gif">;
<P>
(3) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img94.gif">, iff
<IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img95.gif">, <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img96.gif">;
<P>
(4) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img97.gif">, iff <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img98.gif">;
<P>
(5) <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img99.gif">, iff <i>F</i> = 0.
<P>
Here, indices <i>a</i>,<i>b</i> are from 1 to <i>r</i>, <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img100.gif">, <i>k</i> is an
arbitrary number <IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img101.gif">, and the above operators have the
following representation:
<P><IMG BORDER=0 ALIGN=TOP ALT="" SRC="http://ej.iop.org/images/0305-4470/30/6/004/Full/img102.gif"><P>
 
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