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Attachments: Mathematic: Rate of progression on a curve
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Mathematic: Rate of progression on a curve

  • Post #1
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  • First Post: Mar 24, 2011 1:02pm Mar 24, 2011 1:02pm
Hello

Mathematic rules are way back in my memory.

I want to caculate the rate of progression on a curve.

The curve is from an adx indicator. before turning down, the indicator as slowed down the curve. If i could caculate the progression of the curve, maybe i could enter in the market more precisely

Hope I'm clear enough with my not-so-good English

Martin
Attached Image
The "rate of progression" I think you are referring to would be the rate of change of that particular indicator and those settings.

Rates of Change is the concept of literally, how fast an amount is changing. This is the branch of mathematics called calculus. It's not very difficult to learn and is an excellent tool to help program for testing the statistical significance of your insight.

If you are interested in learning opencourseware is available from Mit or Stanford. But a VERY useful resource is http://www.khanacademy.org/. Very good explanations and makes it easy to catch up on topics.

Good Luck
  • Post #3
  • Quote
  • Edited at 3:47pm Jul 10, 2011 5:31am | Edited at 3:47pm
Rate of change is simply dy/dt or y2-y1/t2-t1, t2-t1 will always be equl to 1 if you sample equal 1 unit distance (i.e. daily). So it is simply price2-price1 at each step. Notice at the inflection points (peaks plus and minus), dy (slope) is approximately flat so the rate of change approaches zero before transitioning to and through these inflection points. This is exactly what you are asking for, as I understand it.

http://i51.tinypic.com/21jtx7o.jpg

Also notice rate of change is constant on the downward slope, as each step has equivalent roc during that period.
Keep in mind this doesn't guarantee a future inflection point (as you are considering)... only a potential one.
It could just as easily go flat and transition right back upwards again.
Quoting arjfca
Hello

Mathematic rules are way back in my memory.

I want to caculate the rate of progression on a curve.

The curve is from an adx indicator. before turning down, the indicator as slowed down the curve. If i could caculate the progression of the curve, maybe i could enter in the market more precisely

Hope I'm clear enough with my not-so-good English

Martin
don't know what is really difficult there. you take "point 2" / "point 1". so, if your indicator shows at point 1 the value 60 and at point 2 the value 80, then you divide 80 by 60 and get 1.33 as a result. That should correspond to the rate of change.

If I am wrong, please correct me.
Quoting Custos
don't know what is really difficult there. you take "point 2" / "point 1". so, if your indicator shows at point 1 the value 60 and at point 2 the value 80, then you divide 80 by 60 and get 1.33 as a result. That should correspond to the rate of change.

If I am wrong, please correct me.
That's exactly what ROC does (could it be that MT4 lacks this oscillator?)
However, it seems as if @arjfca http://www.forexfactory.com/images/buttons/viewpost.gif is looking for [something equivalent to] the second derivative of price: that tells you not how fast price is changing (like momentum or ROC), but how fast the indicator is changing. To emulate the second derivative, you might want to apply the momentum indicator to the momentum indicator (which is really simple in MT4):

The red line shows an instance were momentum (blue line) is increasing, whereas the momentum's momentum (gold line) is already starting downward.

Of course, this is not exactly a derivative; in fact, you cannot take the derivative of price, as it is not a continuous function.
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I cannot see how it would be the second derivative. The question is referring to the rate of change of an indicator. I have been using rate of change instead of derivative because we are now dealing in discrete functions.
Quoting Br_pippin
I cannot see how it would be the second derivative. The question is referring to the rate of change of an indicator. I have been using rate of change instead of derivative because we are now dealing in discrete functions.
Although you could use the second difference (discrete version) as a measure of deceleration, notice that my illustration already showed the first difference is sufficient to accomplish what he wanted.

Also, the measure on a noisy price is next to useless. It needs to be applied to a relatively smooth curve to have some use; otherwise there will be numerous faulty signals due to noise. His indicator in the first post appeared relatively smooth and would be more suitable then raw price.
The discussion was not whether incorporating rates of change and possibly even diving into integrals was a viable strategy for that indicator. I was responding to the question. Also, this is a necessary to step towards programming a strategy like this. Where the insights can be quantified and back-tested.



For the original poster-

Just like anything else in forex there are tools in your mathematical toolbox which can be applied accurately and in the wrong context. Historically speaking, while your insight may be discretionary and work for you, the Renaissance Technologies and GETCO's of the world along with more than a few Phd's have probably already used every permutation of that indicator given varying marketing conditions i.e volatility, flow, liquidity, etc. and probably on MANY more securities and cross pairs.

But I still recommend the Khan academy!!!!
  • Post #9
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  • Last Post: Jul 10, 2011 10:05pm Jul 10, 2011 10:05pm
Quoting jamjamjam
Also, the measure on a noisy price is next to useless. It needs to be applied to a relatively smooth curve to have some use; otherwise there will be numerous faulty signals due to noise. His indicator in the first post appeared relatively smooth and would be more suitable then raw price.
It's unclear (at least to me) whether the OP is after the first or second derivative though my guess is the slope, aka first derivative or velocity. That aside, smoothness of the source data is important as you point out regarding what type of output will be produced. There are additional formulas which have been developed to include more input points than two for both velocity and acceleration and which tend to produce smoother output results. The source of these is "The Science of Financial Market Trading"

For instance, cubic or four point velocity can be defined as:

y(n) = (11/6)x(n) - 3x(n-1) + (3/2)x(n-2) - (1/3)x(n-3)

Cubic acceleration may be defined as:

y(n) = 2x(n) - 5x(n-1) + 4x(n-2) - x(n-3)

In the above formulas x would be the ADX, and n would be the bar number of the ADX where the slope is to be calculated.
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