Bitcoin's Logarithmic Regression and What it Says About the Chances of a Bull Market

in #bitcoin2 years ago (edited)

I was gandering over crypto related news today when I stumbled upon this tweet from a fellow with the Twitter account name Awe & Wonder (I will refer to him as Mr. Awe from here onward), sharing the below image:

([right click + view image] for a bigger image)

This led me down a rabbit hole that eventually uncovered a real gem of an article that's directly related to that chart. You can read that very article by clicking on the following Medium link:

In that article, Mr Axe compares BTC's current price trajectory to that of Facebook's user growth, as a young and growing company, and draws several compelling parallels between the two. At two different points in this October 19th, 2018 article Mr Axe states:

BTC’s long-term trend is growing at a statistically significant rate of 5.04% per month and projected to hit $50,000 by the end of 2022. The 50% confidence interval, in this case, is a range between $28,000 and $85,000 at that point in time.

One can speculate that the surge of growth in users seen between 2007–2008 is yet to happen in the cryptocurrency space. According to Willy Woo, the space is currently somewhere in the early adopters phase.

I STRONGLY suggest that you give it a look for yourself.

Back to the chart...

As Mr. Awe also stated in the aforementioned article:

...logarithmic regression has proven itself to be the best forecasting tool for BTC. Exponential regression overshoots actual growth rates over long time horizons...

Having an r-squared value of 0.93, I tend to agree with his conclusion. Of the many models that we can try to fit to BTC's current historical price data (linear regression, exponential regression, no correlation, etc) the logarithmic regression line plotted on the chart in the above image (red line) seems to be it - it's the fit!

What's in the bo-o-o-o-o-o-o-o-o-oxxxxxzz!?!!!

That box shows the price range in +/- percent relationship to the "line of best-fit" (the aforementioned logarithmic regression line, which I will refer to as simply "the line" from now on), complete with some confidence interval bands, calculated using all of BTC's current price data.

The scribbles within that box are what is of the most interest for me. Because, as I'm sure you've already noticed, price has a tendency to explode up to and then quickly beyond those upper bands (high end confidence intervals) any time that price breaks above the line and, in case you haven't noticed, price has just BROKEN ABOVE THAT LINE!!!

For REALZ!!!

Hopefully Brad Pitt finds that to be good news. I feel bad for poor Morgan Freeman, having that gun pointed at him.

Upon further investigation

The more observant among you may have already noticed that price has so far held a trend of reaching lower and lower (in percent terms) above the line with each progressive parabolic (moonshot) move, from 957% in 2011 to 833% in 2013 to 475% in 2017. Mr. Awe had these things to say on this phenomena (from that same article):

...similar to Facebook’s adoption S-curve, BTC is increasing in price at a decreasing rate.

The height of the green bull cycles are logarithmically proportional. The volatility to the upside is decreasing by a ratio of .72 log units each cycle. Same concept applies to the drawdown that followed (.31). Volatility to the downside is also decreasing proportionally. The width of the bear market (.28) is increasing proportionally due to the width increase in bull cycles. Considering that price is increasing at a decreasing rate, it’s reasonable that a lower rate of growth takes more time to cover the same “ground.” Applying this concept to the current bear market, an identically proportional fractal suggests that the highest odds for the next bull cycle is around mid-2019.

That last line (remember, it came from an October 2018 article) seems to fit with what we're witnessing in price. Here we are at month 5, one month away from exactly mid-2019, and the bull very much appears to be at full charge and ready to take out overhead resistances.

Not only do we have evidence, based on the logarithmic model, that the bull-market has begun, but we also have an idea as to where price may ultimately reach before the next bull/ bear cycle ensues.

What's that price? Tell me the price!

Get Brad Pitt to ask me with a gun in his hand and I'll give it up, otherwise hit the road, Jake!

I kid, I'm only kidding...

Unfortunately, I don't know the specific formula to the line, as it's far too small to see and has far too low of a resolution to uncover even with the highest zoom settings (see if you can make out what it says along the very bottom of the chart that I supplied), so I can't get too fine on my estimation.

Also, three data points isn't an ideal amount to work with when it comes to statistical significance, but, regardless, I decided to plot the three price highs that I mentioned (percent value above the line) to calculate a linear best fit line of y = -241x + 1,237, where x equals the number of times that one of these bull market cycle highs are reached and y represents the percent value that we "should" expect above the line (for any given x). This gave an r-squared value of 0.9272 which actually isn't too shabby, but it would be unwise to assume that this means that it has strong predictive value considering how small of a sample size produced it.

That having been said...

The results?

Well, plugging 4 into that formula (as this would now mark the forth high above the line) we get:

y = -241(4) + 1,237 = -964 + 1,237 = 273,

So we should "expect" around a 273% advance above the line when it peaks.

The question is when will it peak and where will the line be when that happens? Being that I'm rather lazy and don't have the precise numbers on what the best-fit logarithmic regression formula are or how long it takes between peaks and their relationship to the last time that it happened, the best that I'll offer is a guesstimate based on observations of the chart that Mr. Awe supplied us all with.

Yeah, sorry for not being a decent human being :( I ain't got time for that ;)

Going back to that chart (and, please, feel free to follow along with me and see if you agree)...

It seems as though it takes BTC about half of a year to reach it's new all-time high after breaking positive (above the line), which is effectively the new cycle high that marks the next bull/bear cycle, the value that we're after. That puts us at roughly the middle of November 2019.

The red line appears to be just above $10K, perhaps $15Kish (?), which puts us low estimate ($10K * 273%) around $27K to maybe ($15K * 273%) around $41K, more moderate, to perhaps even a few 10K's higher on the extreme side, according to this model, interpreted through my eyeballs. Of course, we can get far more accurate if we have those numbers that I mentioned earlier (the actual formula and what-have-you).

It's stated in Mr Axe's surely famous (by now) article that...

[bitcoin is] projected to hit $50,000 by the end of 2022. The 50% confidence interval, in this case, is a range between $28,000 and $85,000 at that point in time.

, for what it's worth.

However, we should not place too much credence in what this, or any other model, has to say about price projections with as relatively little data as we have to make these types of predictions. As Mr. Axe, himself, concluded (again, in the supplied article that I've now quoted to death, no doubt):

...logistic analysis requires very strong assumptions regarding the inflection point and estimated max price. Again, any type of analysis should not be used in isolation. Rather, it should only serve as a fraction of evidence to come to a sound conclusion.

Do with this what you will

But remember, I am NOT a financial advisor. Have a mind of your own. Don't be a weak puppet, to be pushed around by those who appear confident. Be the strong human that you are and use those faculties that God has provided you to form your own opinions and conclusions, so that you can act on your own strength and know that you've acted RIGHTLY.

Please consider the above suggestion. Regardless, I have faith in you and I wish you endless well being, peace and joy. Oh, and you may also have yourself a good day!

Peace :)


Constructive criticism and pointing out of errors in any of my calculations/ conclusions are welcomed.

Okay, NOW you may peace out :)


I like it, the theory and research is sound enough for me to keep it in the back of my mind while calculating decisions.

I think it's always a good idea to try to be on the side (bias) with the highest odds of being correct and that's where a model like this, that has a provably high statistical significance, is useful, IMO.

It can tell us with a relatively high degree of certainty what range of prices we can expect at X time in the future. There's no way to know for sure that price will continue to have this relationship to the logarithmic regression line, but it HAS had a strong relationship with it so far (as indicated by the r-squared value) and the data so far suggests that this relationship (and the patterns that come out of it) is still in play.

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