In the older days of engineering, I'm talking about slide-rule era, simplifying assumptions were a very big part of everyday life. They made it possible to cope with things that were far too complex to deal with otherwise. Simplifying assumptions came with their own side effects, one had to keep in mind all of them to make sure they didn't take one into blind alleys...
Piecewise Linear Approximation was a good way to describe a curve of unknown properties.. A chart would be produced, then it would be recreated with as few straight lines as possible and the straight lines could be described in very simple terms of slope and endpoints. Slope could be thought as representing the f' averaged over the length of the piece-line, that concept is a big help in deciding just where/when to place the lines' begin-end points...
Chart geometrics combined with volume analysis might be as good as it's ever going to get... draw trendlines, draw parallel lines that form the channels, look at price movement within the channel interpreted by volume to sense when the channel is ending and you are good to go... it is a representation of Signal +Noise and the Noise helps to interpret the channel... the only problem is that sometimes a trend gives off a very clear signal that it's ending, but it's only plateauing and will continue on... I'm still working on that part of course, it's the thorn in my trading side and it takes a bite out of too many trends for me...
If somebody could work out some math for differentiating an impending trend reversal and an impending consolidation I would love to hear about your work via forum or PM. Possibly that math does not exist and a "coping skill" would be a better answer, maybe when the end of trend is detected it's best to try to exit at the best price one can get and wait for confirmation of the next move...
Piecewise Linear Approximation was a good way to describe a curve of unknown properties.. A chart would be produced, then it would be recreated with as few straight lines as possible and the straight lines could be described in very simple terms of slope and endpoints. Slope could be thought as representing the f' averaged over the length of the piece-line, that concept is a big help in deciding just where/when to place the lines' begin-end points...
Chart geometrics combined with volume analysis might be as good as it's ever going to get... draw trendlines, draw parallel lines that form the channels, look at price movement within the channel interpreted by volume to sense when the channel is ending and you are good to go... it is a representation of Signal +Noise and the Noise helps to interpret the channel... the only problem is that sometimes a trend gives off a very clear signal that it's ending, but it's only plateauing and will continue on... I'm still working on that part of course, it's the thorn in my trading side and it takes a bite out of too many trends for me...
If somebody could work out some math for differentiating an impending trend reversal and an impending consolidation I would love to hear about your work via forum or PM. Possibly that math does not exist and a "coping skill" would be a better answer, maybe when the end of trend is detected it's best to try to exit at the best price one can get and wait for confirmation of the next move...