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...
For those of us that actually trade, knowing immediately when a bull turns to consolidation, consolidation turns to a bull or bear or a bear turns to consolidation (all in real time) is the key. Measuring a trend is worthless because each one doesn't last a specific length of time and there is no way to predict it's end in advance. Buys are weighted in a Bull Trend. Sells are weighted in a Bear Trend. Scalping or taking a nap is weighted during consolidation.
Keeping stats of the swing lengths, min , max, avg, and duration is an important piece of the pie for me. In the past 10 days the avg upswing length is A. the min swing length is B. the max swing length is C so the current swing I am in should go to at least A. I will expect B and be cautious near C. It's good to know when the buy or sell signals will most likely work .
How do you deal with the fact that the efficiency ratio gives the same results for step functions as for diagonal lines? I spent some time working with it some time ago but abandoned it as a trend measurement. EDIT: I didn't mean this to challenge your use of it as a trend measurement. Maybe we should first define 'trend' so we know what we are measuring?
OK, here's my definition(s): A trend is a propensity for time-series data to be unidirectional, or to at least move significantly more in one direction than in the other direction. Financial trends are mostly transitory, coming and going unpredictably. A trend in which data is predominantly increasing is an UPTREND. A trend in which data is predominantly decreasing is a DOWNTREND. A trend is always either an uptrend or a downtrend. There is no such thing as a "lateral trend" or a "sideways trend"; these are oxymorons. When data is non-trending, it is said to be "noisy" or "choppy." In other words, noise aka The Chop is the absence of trend. *** You're right about the KER being flawed and I was waiting for somebody to pick up on that. The big flaw of the KER is that it only measures net trend. It tells us nothing about what's going on between the endpoints except for sizing the denominator. I'll put this out for anybody to answer: Would an accurate measure of how much of a given time-series interval is trend be of use to your trading? A few here seem fixated on trend duration. I'm not talking about trend duration, I'm talking about the things in the OP: trend strength and trend quality. Specifically trend quality in the above question.
This thread is about measuring trends. When you measure something, you get a number. This number is known as a measurement. There are no measurements produced by channels and trendlines. They are utterly worthless for measuring trends. Maybe they can detect trends, but that is not the same as measuring trends.
When I use a technical indicator, I automatically get a number aka a measurement. You're telling me I have to jump through all sorts of extra hoops to squeeze some sort of number out of trendlines. This comes across as archaic at best in the age of automated trading strategies. That's not even accounting for the fact that trendlines are almost always useless for short-term trends. Whereas an indicator can generally be applied to a trend of any duration.