relative smoothness over range

[bernie_c]

I would like to know the relative smoothness of a plot over a some range. What I have been doing is noting the difference in slopes (pseudo angle) of adjacent segments over the range. If the maximum pangle is less than my thresh then the range is smooth enough. The problem is when at least one segment in the range has a different sign than the rest. With trig I would just roll around the circle 180 degrees. These are not real angles. Any ideas?

[NinjaTrader_ChelseaB]

Hello bernie_c,

If you are looking for a formula to find this I will not be able to assist but this thread will remain open for the community to offer help.

If you are trying to find slope, use the Slope() method.
http://www.ninjatrader.com/support/h.../nt7/slope.htm

If you would like a link to a list of professional NinjaScript Consultants who can create this formula for you, please let me know.

[koganam]

I would like to know the relative smoothness of a plot over a some range. What I have been doing is noting the difference in slopes (pseudo angle) of adjacent segments over the range. If the maximum pangle is less than my thresh then the range is smooth enough. The problem is when at least one segment in the range has a different sign than the rest. With trig I would just roll around the circle 180 degrees. These are not real angles. Any ideas?

Maybe then you should be looking at values of the normalized slopes, and not muddying up the analysis with angles?

[bernie_c]

I agree koganam. I don't really care about angles. I just use the word angle for lack of a better one. I realize the relationship of one slope to another is not a real angle, at least not in the classical sense. That is why I am a little stumped. Well, that and I am up way too late

What exactly do you mean by normalize?

[Harry]

Normalization is a mathematical process. This is done in three steps.

(1) First you need a vectorspace (a set of data points) and the define a norm (a mathematical formula that allows to measure the distance).

(2) In a second step you apply that norm to your vectorspace (calculate a distance for those data points).

(3) You divide momentum by the result of the calculation under step 2.

Mathematical formulae that can be used as a norm are the standard deviation and the average range or average true range. Both standard deviation and average range / average true range can be calculated directly from your data points.

Example:

Let us us the standard deviation for nomalizing an oscillator with a bad behaviour. Bad behavior means that the indicator is not normalized and does not pass the c-test by trader Willliam Eckhardt. For example

-> RSI, Stochastics and TSI are well behaved (already normalized) and pass the c-test
-> Momentum, ROC or MACD are not well behaved and require normalization

For the sake of simplicity, I will show one possible normalization process for the momentum indicator.

-> calculate the standard deviation for the last N (for example N= 100) data points
-> then calculate the difference from current close and mean (=SMA) of the last N data points and divide it by the standard deviation

The result is something well known and called the Z-Score of momentum. The chart below shows momentum and the normalized momentum (normalized over the last 100 bars).

[Harry]

More details on normalized slopes can be found here:

https://www.bigmiketrading.com/ninjatrader-programming/17859-coloring-indicatorline-slope-questions-optimal-coding.html

The BollingerUniversal indicator here

https://www.bigmiketrading.com/download/ninjatrader-7/indicators/626-download.html?view

allows to color midband and channel according to slope. This indicator does not use the standard deviation for normalizing the slope, but it uses the average true range. As long as the slope of the bands is within a range that is expressed as a multiple of the average true range, it is considered flat and plots yellow. Only when that range is exceeded, the indicator lines will plot green (upsloping) or red (downsloping).

It would have been possible to build the same indicator by using the standard deviation as a norm.

[arbuthnot]

I would like to know the relative smoothness of a plot over a some range. What I have been doing is noting the difference in slopes (pseudo angle) of adjacent segments over the range. If the maximum pangle is less than my thresh then the range is smooth enough. The problem is when at least one segment in the range has a different sign than the rest. With trig I would just roll around the circle 180 degrees. These are not real angles. Any ideas?

Hi Bernie

Very briefly if you're trying to analyze smoothness over an interval.

In calculus, you'll remember that with polynomials (f(x) = x^3 + Ax^2+Bx+C, etc.) when you take differences (f(x+a) -f(x)), they become less chaotic and eventually the diffs of the diffs, etc., become zero: this is exactly what the differentials do.

So my idea, which may lead nowhere at all, is to set up a loop for the first-order differences, then repeat the process a few times. The more 'ordered' the n-th diffs are (or the smaller the weighted average difference preferably) may be evidence of the smoothness of the original price data over that interval.

Just an idea!

[koganam]

I agree koganam. I don't really care about angles. I just use the word angle for lack of a better one. I realize the relationship of one slope to another is not a real angle, at least not in the classical sense. That is why I am a little stumped. Well, that and I am up way too late

What exactly do you mean by normalize?

Harry's explanation is very good, but concentrates on the mathematics behind normalization. Here is an explanation of the principle behind the need to normalize slope data.

A lot of folks like to think of a slope as representative of an angle. This is only really true if the slope itself is dimensionless, because in that case, the two parts that make the slope, the rise and the run are being measured in the same units, (usually on the same linear scale). Remember that an angle is a representation of distance/distance.

Rise/run on a chart is money/time, which is not a dimensionless quantity. As an example, take a rise of $2 over 10 bars. The slope would be calculated as 0.2$/bar. However, does this represent the same information on a $1000 index as it does on a $10 stock? Evidently not. So we have our measure being inconsistent as an indicator.

The solution is to measure this putative slope as a multiple of some measure of the equity itself, and how fast it moves. The process of doing so is called normalizing the resulting slope, as it now is a measure of the absolute slope as a proportion of the "normal movement" for each equity. Such measures include such things as Harry identifies: average range, average true range and standard deviation being the most usual ones.

On a philosophical note: What we traders call momentum, should properly be called speed, as it represents only two quantities, movement/time: there is no representation of mass. Calling it momentum tacitly assumes a mass of 1. If called speed, then momentum would properly be a measure of a portfolio representation, which would then include the number of shares as representing the mass. But, never mind, that is just a mathematical purist talking. The mass of traders think of it as momentum, so so shall we.

[bernie_c]

Thanks for all your detailed responses. I learn a lot listening to you folks. I apologise for starting this bit of white noise. My original intuition was correct.

All I need to know is how smooth two adjacent segments of a plot are. Subtracting one slope from the other gives a relative indicator of straightness. 0 = straight ( both segs have same slope). The larger the number the less straight. This number is not an angle, but it can be used to compare relative straightness of segment pairs.

I ended up using Print() to print out a bunch of seg slopes. I then copied them into a spreadsheet and proved the concept. Worked just fine.

Thanks again.