Quote from braincell
If anyone's interested in math, I have about 70 pages of charts (distribution analysis, normalization values, intra-channel price harmonics) from my analysis results. They look pretty, but I'd hate to elaborate what they mean hehe. Useful I know. The normalizations are useful for automated trading and quantifying strength/speed/etc of constructed trend channels.
Interesting⦠First time see some real quantitative works.
For example:
1) construct trend channel,
2) find width in absolute terms
The width can be defined as the distance between the two parallel lines form the channel (then the line segment of this distance is perpendicular to these two parallel lines), or the price difference between the two interceptions of the trend lines with any bar and its extension? I guess both definitions would be OK.
3) find width in % terms
Good. Thus convert the absolute width to relative width in % (dividing width by price. Since a channel contains many bars so my guess is that the price used could be the average price of the closing prices of these bars)
4) normalize width percent
Stop. You did it too soon here. Each width is associated with a different volatility. I saw you next step is to expend them on volatility spectrum. It is logical confusing to put all widths together to normalize them now. You will do normalization in you last step. In general, donât do normalization twice on the same set of data.
5). find distribution of normalized width % accross volatility levels
Very good. Now we have a 2D graph. The horizontal axis is the volatility level. The vertical axis is the percent/relative width. (not normalized yet)
6). adjust for volatility to get a linear mean value for distribution
Excellent. Please let me know if you donât use linear regression method. Though I did not do these analyses but I can image that the data points form a band/cloud from lower-left corner to upper-right corner since narrower widths are often associated with lower volatilities and wider widths come mostly from the higher volatilities. Linear Regression is idea method here. Yes, the LG line can be served as mean value. Think how wonderful that only two numbers â a slope and a intercept can represent N mean values where N is the # of bars in channel and it is usually several dozens up to hundred.
7). then create a normalized distributed adjusted for volatility table to get linear values, and voila
Done.
I donât know how big your table is. It should been keeping the balance between how may data points you have and how accurate the normalization will be. There are few other methods to normalize it that require almost no or small tables in order to save computer memory space should this become an issue.
Useful, though a little noise at extreme ends but if used properly, can tell you exactly how "strong" a trend channel is. Anyone else do this kind of math?
Anyway, now you have a non-biased, volatility calibrated math tool to help you better enter/exit market once a channel is observed. You called âlittle noiseâ at two ends of the width distribution are not unusual. Rather, it is common for lots of other analyses. Wall street calls it the FAT TAIL and blamed it the cause of recent economy crises. Theoretically the probabilities at the extreme ends should be too little to pay any attention but in reality it is not the case as the market is moved by human beings.
There are probably two indicators I can think of âstrongâ a channel you mentioned:
a) In math called the âslopeâ of the channel, in physics called âspeedâ or âvelocityâ, Wall Street call it the âmomentumâ
b) In math/Geometry called the âwidthâ of the channel, in physics/mechanics called the âamplitudeâ of wave/oscillator, I call it âpersistenceâ or âreliabilityâ of price movement along the trend line direction.
You have done a great work. Have you done anything about Channel duration analysis?
