Since I made that chart, i'll say use it with caution. If you make any trading decisions based on that chart you are on your own. It only contains data for part of the period, after the first large bubble in 2011. It also has to be expanded with a S-kind of ending at the top since it will obviously flatten out when saturation is reached. But it gives the best fit to the data for that time period -- under the assumption that a single function generated the data during the entire period.
Fixed
Not attacking you, by the way, I appreciate your input. Just that it's a pet peeve of mine: pointing out that despite all the other assumptions (remove outliers or not?, which period to use for input?, exponential function? double exponential?), the assumption that it is exactly one function we're looking for is perhaps the biggest (simplifying) assumption of them all.
Yes, I agree. It's the best "simple" function I have found that best represent the data in this period. I'm sure there is more to it than this. Maybe step functions and
dampening underdamped oscillators could be added to have a more detailed description including the bubbles since there seems to be a time pattern to them. Some others have suggested steepening linear log functions (
https://bitcointalksearch.org/topic/24-feb-report-bitcoin-price-theory-proposal-394221, and others stick to the full range linear function with monthly price averages (rpietila
https://bitcointalksearch.org/topic/monthly-average-usdbitcoin-price-trend-322058). And maybe the double exponential plot suggested in my graph is even to conservative, only time will tell. It's meant as an input for debate.
I've seen them both. gbianchi models price as a function of total no. of btc addresses unless I'm mistaken. Not totally dumb I'd say, but in the end, I'd bet no. of addresses and price are not independent. And rpietila is using the most "traditional" way of a log linear model (line of best fit) unless I'm mistaken. I strongly doubt that approach is useful for active trading, it's shown itself to be off by more a factor of 10 (!!!) at times.
I understand the desire to find the *one* function that fits them all, but even trying to find a more complex function like an (under)damped oscillator is perhaps not the best way to go about it: I personally believe there is no way around the idea that, at different time periods, different functions govern btc price. The trick is of course to limit that number in a systematic way, and to avoid overfitting.