Trend, taken as a slope as in "trend line," is the average rate of change of price with respect to time. A question like, "Do trends exist?" is an oversimplification. The real issue is whether or not future price can be determined on the basis of past price action. Just because price has drawn itself in a certain pattern over a previous timeframe, doesn't mean it has done so due to a tendency that will continue in the future. So, for the purpose of making money, the answer is that trends don't exist.
That looks like a non sequitur - how do you make the leap from what you said in the first paragraph, to your conclusion?
You're not on topic with the rest of us like hank, hanseng.... But write me a code that draws the trendlines that you exactly do with hand, then we'll be on the same page. Once we have a common basis of what we can agree to what a trend is... then we can actually test the statistics of whether the "trend" exists or not. "Do trends exist?" is the same as asking "What is a trend?"... It's not about abstraction but actually clarifying (at least for the sake of discussion). You might use trendlines, others may use moving average, linear regression, etc. etc. as a basis. What would be a common definition of a trend? For a Turtle trader, it would be catching some outlyer out of the "normal". Playing with Risk Management and distribution. For a swing traders, it maybe some preliminary setup. Playing with probability. There are different points and perspectives that has to be considered based on the edge you are trading or talking based on. I'm sticking to Turtle's sense because JWH, Dunn and others trade based on mainly what is close to the Turtles. Without knowing this... you're not on the same page.
Okay, what is your definition of "trend" according to which price action within one timeframe implies a causal tendency that can be extrapolated to indicate future price?
So you want A = B = C ???? My answer to that is "A is A". Added: OK... that's kind of a harsh answer... Well... you seem to over-use hard words so I'll just condense what you wrote to "High Probability Setup".
What would be an instance of "trend," as you have defined it, where price action within a certain timeframe implies a causal tendency that can be extrapolated to indicate future price?
*sigh* So a definition changes to instance. I don't know you tell (show) me. I'm not sure whether your quote "where price action within a certain timeframe implies a causal tendency that can be extrapolated to indicate future price?" = "High Probability Setup"
My definition was: Trend is the rate of change of price with respect to time. It's possible that this concept is not officially defined in the trading world.