Topic: Logarithmic (non-linear) regression - Bitcoin estimated value (Read 117626 times)

A really nice observation, but BTC cyclic nature looks much better in a Log-linear scale, since time is often a linear thing (IMHO).
Like in the example here

https://i.ibb.co/m4kYCsq/BTC-Plan-52.png

Amazingly, this model is still valid today. Not in its exact formulation but in the equation itself.

It turns out it is actually a POWER LAW (or SCALING LAW), the Trolololo formula can be written, with some simple algebra, as Estimated Price=A * (days from GB)^n, where GB is Genesis Block, A is 10^-17 and n=5.83.

Trolololo had instead log10(Price)= D *logn(days from GB)-C, the values for D and C that Trolololo regression gave are a little off because he had less data and also calculated the fit just after the top of one of the cycles and that skewed the result. Also, the use of 2 different logs, one in base 10 and one in natural base threw me off and I could not recognize his formula as a power law but it was indeed a power law.

I'm not sure about Trolololo's background but I guess he didn't know about the significance of Power Laws. Power Laws are really important in science and technology. See this talk to understand why:

https://www.youtube.com/watch?v=XyCY6mjWOPc

But he had a very good intuition that was to focus on how BTC scales up with increments of 10, 100, 1000s. So he used the log10 in the y-axis and noticed that it was not a straight line (that it would be if the growth was exponential) but a curve. He still kept the time in a linear scale so he decided to use a non-linear regression that indicated that the best fit was a log progression in time.

If he indeed plotted the log10 of price and the log10 of days from GB he would have noticed the incredible fact that the price progression then looks like a straight line! That means we are dealing with a power law.

There is no reason to use 2 different bases for the log and it is more natural to use the base of 10.

I didn't give much consideration to Trolololo's model because it seemed initially an arbitrary model (why log progression?).

I worked on many BTC price models but as a physicist, we are trained to plot data that do not fit initial simple linear or exponential models in a log-log chart because another form of natural law that is ubiquitous is a power law of the form y=A x^n.

But it is not usual to plot assets in a log-log chart given almost no asset is a power law.

But as Kepler did when he looked for the laws for planetary motion I decided one day to plot the price of BTC in a log-log chart.

I almost fell from the chair when I realized it was indeed a straight line!

It completely makes sense because BTC is a network and one of the characteristics of networks is that some of their parameters show power law behavior, but it is an amazing fact and something almost nobody knows and for sure not the media or the general public.

It is as a fundamental discovery as BTC itself. I'm not kidding. It means that BTC price is not random but follows a predictable behavior over the long run that is similar to the behavior of mountains, rivers, cities and nations. BTC is a force of nature itself.

I take the credit for identifying it as a power law because as far as I know, I was one of the first people to point out this and to post the discovery on reddit 5 years ago (hcbuger used my idea and popularized it, he quoted my post on reddit but for some reason everybody attributes the power law model to him).

But the credit for the first intuition that BTC scaling is important goes to the great Trolololo with his grandfather model in 2014. Just amazing. Forget about S2F, The BTC Scaling Law is the true law of BTC.

If you are interested this is my first post about BTC being a power law:

https://www.reddit.com/r/Bitcoin/comments/9cqi0k/bitcoin_power_law_over_10_year_period_all_the_way/

And here is an update after 5 years from that first post:

https://www.reddit.com/r/Bitcoin/comments/18z04kp/15_years_of_btc_power_law/

Also, you can follow me on X with updates on the model and its significance here:


https://twitter.com/Giovann35084111








 

Hi Sergii,
It turns the model of Trolololo is nothing else than a power law. He wrote the formula, log10(Price)=A*ln(days)-C but this can be rewritten as Price=10^(A*ln(days)-C) or Price=days^(Aln(10))/10^C or price=B*days^n where B=1/10^C and n=A*ln(10).
It is a big deal because a power law first of all looks like a straight line in a log log graph and BTC looks exactly like that. And also power laws are very important in science. Many phenomena in nature follow power law. I will write soon a medium article on this topic. I think Trolololo discovery was the most important in BTC history (well together with my realization that it is a power law not some random formula).

The model was created by me on Reddit, https://www.reddit.com/r/Bitcoin/comments/9cqi0k/bitcoin_power_law_over_10_year_period_all_the_way/ . Burger quotes me but for some reason everybody attributes the model to him. He did a good job in popularizing it but it is not his model. Anyway, it turns out that the obscure math Trolololo uses is actually a power law. Nobody observed this until recently. It would have been much more impactful if he had written as a simple power law, Price=A*days^n. That is it. Trolololo parameters were a little off because of the little data collected at that time.

Just noticed www.moonmath.win is up again. (The model hasn't been updated, though.)

Bitcoin price prediction 2023 - 2033 "lowest" price based on log log power law devised by Harold Burger.

Forecasting Bitcoin's Minimum Value. This provides an estimate of the "lowest" potential value, expressed in US Dollars (USD), for a single unit of Bitcoin (BTC) based on the logarithmic power law model developed by Harold Burger. It's crucial to underscore that these figures represent the absolute minimum values, suggesting that actual prices could only be higher.

Please approach these predictions with an understanding of their inherent uncertainty.

2023: $16,000
2024: $24,000
2025: $35,000
2026: $50,000
2027: $70,000
2028: $95,000
2029: $125,000
2030: $165,000
2031: $225,000
2032: $285,000
2033: $375,000

https://bbcdsatoshi.com/Charts/

Useful video on YouTube called "The Bitcoin Power Law Growth Corridor" by Chad Thackray. Well worth watching.

The description says: We implement a model popularised by Harold Burger, which uses a log-log chart of bitcoin and then applies linear regression to establish a long term corridor of price action, which has worked well over the past 10 years. It's a useful indicator to zoom out and see the big picture, without getting worked up over day to day price action.

https://www.youtube.com/watch?v=wfi-bst4hmA

Great to have you back Trolololo

It seems like nowadays everyone should have their rainbow chart for BTC price ))

https://www.cryptocompare.com/profile/yurets.zh/#/activity

I prefer the lookintobitcoin one, but, unfortunately, it only updates at a resolution of one day, so it isn't necessarily showing the lowest price points (or, if it does, it doesn't show them in the middle of the day while it's happening).

That is correct.

@dragonvslinux

Concerning the model, I believe the curve should be updated after adding new historical data to it. At least that is what I do to build the plot that I use for my forecasts.

Fair enough I hear ya. Looks like blockchaincenter have had a botched version for sometime now then, as clearly it's very different than how it should be, for whatever reason. Thanks for pointing out which one is more accurate, I'll stick to the lookintobitcoin version from now on, even if it's not clear if this is based on the original model:


It seems they are almost implying this is a different version of the rainbow chart (no copyright) that's based on logarithmic values, but not necessarily the "original hard-coded version". If you look more in-depth, I think you'll find it is slightly different (look at the March 2020 lows as well as current price), because ultimately they've made a good effort to remove any confirmation that they using the original arbitrary version.

This is why I said it's not arbitrary anymore, as there are two versions (if not more), even if it should be but only when based on the original (that has no copyright).

Probably that does not work for the Newbie users

https://i.ibb.co/wLTgwtw/BTC-Plan-29.jpg

Like I said, just change the file extension to jpg (the server already has it) and put it inside the img brackets and it will show the image:

You didn't get me. The Log curve is an approximation of price history (logarithmic regression). That is the scientific part.  But the rainbow is made by duplicating that curve parallel to itself with certain intervals that are not somehow "scientifically" linked to volatility, ATHs ant Lows.

And it does not look like they have modified the curve either. Here is my view of the trend as for now

https://i.ibb.co/wLTgwtw/BTC-Plan-29.jpg

Clearly it's not arbitrary when LookIntoBitcoin have modified the logarithmic curve, and haven't referenced the fact it's arbitrary or lacks any scientific basis. Probably because it's a mathematical based curve, nothing to do with science. The irony being that a logarithmic curve in itself isn't arbitrary, it's simply how you style it (connect the dots), even if the original remains arbitrary and unchanged.

You should always remember what is written on one of the referenced web pages: "The color bands follow a logarithmic regression (introduced by Bitcointalk User trolololo in 2014), but are otherwise completely arbitrary and without any scientific basis."

There's actually two slightly differing models here, if not more online by now, not just the blockchain center version of the chart.

1. https://www.blockchaincenter.net/en/bitcoin-rainbow-chart/
2. https://www.lookintobitcoin.com/charts/bitcoin-rainbow-chart/

I reference this as the LookIntoBitcoin version looks more relevant, as factors in the March 2020 low more accurately, as seems to have been adjusted to include it.



This chart also gives a bit more room to the downside potential, with the lower band at $16.2K whereas the other is around $18K if not mistaken.

I think it works if it's a jpg.