If we pretend (which is of course not accurate, which is why I say pretend) that the price follows a Wiener process, so that on each time interval the net change across that interval is a normally distributed random variable with mean 0, where the difference across different disjoint intervals are independent,
well, under that inapplicable model, said "7 different times" wouldn't be independent (while the difference across the first 5 years, and across the second 5 years, would be independent, and so that would count as 2 independent observances of that.
I wonder, if you have such a process W, what would the probability of "For all t in [0,7], W_{t+5} > W_t" be?
It would of course be less than (1/4) because it would imply W_5 > W_0 , and also W_12 > W_5 , which would be independent events each with probability 1/2 , and so the probability has to be at most 1/4 . But I assume it probably has a much smaller probability than that.
If instead of a Wiener process, we model it as a Wiener process with drift, as X_t = \mu t + \sigma W_t , how does the probability of "For all t in [0,7], X_{t+5} > X_t" vary with \mu ? (well, obviously, as \mu increases, the probability goes up, but I mean stuff like "how big does \mu have to be in order for it to not be unlikely?" and "how quickly does the probability increase as \mu increases?", etc. . )
Isn't the point he tried to make that if you've chosen an entry point into Bitcoin anywhere in the last -12 - -5 years you'd still be ahead 5 years later? So that if your time horizon is at least 5 years and if history is any indicator (here is the real fallacy imho) investing in Bitcoin is a good idea?
I was mostly just trying to show why the "it happened twice" makes some sense, (though, it is somewhat stronger than "it happened both times". I just don't know how much stronger. I guess that was the sort of thing I was wondering-out-loud about) and also saying some thoughts that that brought to my mind.
But yes, "it working at any time if you wait 5 years" would be relevant.
I guess I was trying to think about, "what would the chances be of that happening to have been the case purely by chance?". Like, in order to look at how strongly it suggests it will be the same in the future.
I wonder, if you have such a process W, what would the probability of "For all t in [0,7], W_{t+5} > W_t" be? It would of course be less than (1/4) because it would imply W_5 > W_0 , and also W_12 > W_5 , which would be independent events each with probability 1/2 , and so the probability has to be at most 1/4 . But I assume it probably has a much smaller probability than that.
If instead of a Wiener process, we model it as a Wiener process with drift, as X_t = \mu t + \sigma W_t , how does the probability of "For all t in [0,7], X_{t+5} > X_t" vary with \mu ? (well, obviously, as \mu increases, the probability goes up, but I mean stuff like "how big does \mu have to be in order for it to not be unlikely?" and "how quickly does the probability increase as \mu increases?", etc. . )