Logarithmic (non-linear) regression - Bitcoin estimated value

[findftp]

Nice graphics and nice work!  

What software did you use?

Excel.

As Rpietila says, you can do amazing things with excel.

Wow, nice work!
Thread watched and notified.
Just gave a small tip.

[Trolololo]

Added to the OP:
Calculate today's trendline price HERE

Your work is really great. This trendline seems realistic.

Could you provide a date for the one million dollar price ? Or extend your chart a little bit ?

1.000.000 on 06-09-2026

I would like extend the chart to that date, but by excel worksheet doesn't want to. I don' know why.

[Trolololo]

Nice graphics and nice work!  

What software did you use?

Excel.

As Rpietila says, you can do amazing things with excel.

Wow, nice work!
Thread watched and notified.
Just gave a small tip.

Thank you!

[madmat]

Added to the OP:
Calculate today's trendline price HERE

Your work is really great. This trendline seems realistic.

Could you provide a date for the one million dollar price ? Or extend your chart a little bit ?

1.000.000 on 06-09-2026

I would like extend the chart to that date, but by excel worksheet doesn't want to. I don' know why.

Thanks for the date.

Excel is not perfect. Did you reach the line limit ? (1 048 576 lines)

[Trolololo]

What price do you get in 2075? In my opinion the "equilibrium" price of Bitcoin is one of the easier numbers to make rational arguments about (thermodynamics is always on sounder footing than kinetics, etc.).
For example, if you get $1 trillion per BTC in 2075, I would say the model is problematic, however well fitted. If you get something in the $1-10 million range, then you're probably in the ballpark. (these models assume a certain optimism about adoption already)

With only 1550 days of prices, it's quite weird to estimate the value for day #24.098 (01-01-2075).

But let's suppose that the price stays flat at 370 for 5 more years (from today to 01-01-2020).
That would mean we have around 5500 days of prices.
The logarithmic regression would throw a estimated value of 961 k$ by 01-01-2075.

That's a more realistic value than any linear regression model.

[oda.krell]

Nice post & analysis, Trolololo. Following.

I made a similar observation earlier this month in Stephen Reed's thread, about what looked like an increasing time span between reaching the next order of magnitude in network size, but didn't follow up on it (shameless plug to my own post :D).


A question.

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

It seems to fall somewhere between linear growth and exponential growth, and it isn't bounded either (like in Stephen's model). I was wondering if someone with more knowledge on functional growth could answer this once and for all for me, have been wondering about this for a while now. (EDIT: I'm wondering if it could be an instance of so called sub-exponential growth)


A critical remark.

While I personally, intuitively, find a price function with a declining growth rate (like yours) more plausible than the constant growth rate models that have been presented on this forum (i.e. the "loglinear models" you linked to as well), one problem still remains:

Price tends to "jerk around" all those models.

I remember that, late last year, when price exceeded even the loglinear model's predictions, some analysis was posted that suggested a superexponential price function to model BTC price.

Then came the first leg of the 2013/2014 correction, and suddenly the loglinear models were all the rage again.

Now, the correction continues, and you suggest (with good reasons, I agree) a model based on an below exponential growth assumption. But I'm afraid all it takes is another year of bear market (or perhaps, a sudden rally of huge proportions), and we need to re-adjust our assumption for what the "best" growth type for our model is...

Here's what I'm trying to say: I am using technical (i.e. historic price based) methods myself all the time for predicting price on the short term. However, I start to think that, on a long enough time scale, fundamentals govern the price function. So a model like yours (or Stephen's, or rpietila's), that are essentially an extrapolation from an (admittedly well fitted) function on the historic price data might come to its limits.

I am thinking that perhaps the only semi-reliable way to go about mapping the "long term trend" is Peter R.'s way: finding a proxy for network size, and then modeling expected price/mcap as a function of network size.

See for example here: https://bitcointalk.org/index.php?topic=68655.msg9059346#msg9059346

He still makes a number of assumptions (Metcalfe's law, for example), and in a way, his method only shifts the problem (because now we are trying to predict, i.e. extrapolate, network size), but at least his predicted numbers will rarely be so out of tune with reality as the pure time series models can be at times.

[Trolololo]

Nice post & analysis, Trolololo. Following.

I made a similar observation earlier this month in Stephen Reed's thread, about what looked like an increasing time span between reaching the next order of magnitude in network size, but didn't follow up on it (shameless plug to my own post ).


A question.

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

It seems to fall somewhere between linear growth and exponential growth, and it isn't bounded either (like in Stephen's model). I was wondering if someone with more knowledge on functional growth could answer this once and for all for me, have been wondering about this for a while now. (EDIT: I'm wondering if it could be an instance of so called sub-exponential growth)


A critical remark.

While I personally, intuitively, find a price function with a declining growth rate (like yours) more plausible than the constant growth rate models that have been presented on this forum (i.e. the "loglinear models" you linked to as well), one problem still remains:

Price tends to "jerk around" all those models.

I remember that, late last year, when price exceeded even the loglinear model's predictions, some analysis was posted that suggested a superexponential price function to model BTC price.

Then came the first leg of the 2013/2014 correction, and suddenly the loglinear models were all the rage again.

Now, the correction continues, and you suggest (with good reasons, I agree) a model based on an below exponential growth assumption. But I'm afraid all it takes is another year of bear market (or perhaps, a sudden rally of huge proportions), and we need to re-adjust our assumption for what the "best" growth type for our model is...

Here's what I'm trying to say: I am using technical (i.e. historic price based) methods myself all the time for predicting price on the short term. However, I start to think that, on a long enough time scale, fundamentals govern the price function. So a model like yours (or Stephen's, or rpietila's), that are essentially an extrapolation from an (admittedly well fitted) function on the historic price data might come to its limits.

I am thinking that perhaps the only semi-reliable way to go about mapping the "long term trend" is Peter R.'s way: finding a proxy for network size, and then modeling expected price/mcap as a function of network size.

See for example here: https://bitcointalk.org/index.php?topic=68655.msg9059346#msg9059346

He still makes a number of assumptions (Metcalfe's law, for example), and in a way, his method only shifts the problem (because now we are trying to predict, i.e. extrapolate, network size), but at least his predicted numbers will rarely be so out of tune with reality as the pure time series models can be at times.

In linear price axis the trend looks exponential:



But is really a subexponential line, a "lowering" exponential trend.

I suspect that in the very long term (reaching year 2075 i.e.) the linear price axis graph would look like an "S" curve (logistic growth). Pending task...

Edit: no "S" look at all. Looks like a "lowering" exponential trend for any timeframe.
To have a "S" look que should use another regression function, like



Relative to volatility, I also suspect that the tops of the bubbles could fit in a similar logarithmic regression. The same for the bottoms of the bubbles. That could give us an estimation of the roofs and floors of next bubbles.
Another pending task...

[dnaleor]

nice charts

will folow your posts from now on

edit: left you a small tip

[oda.krell]

Edit: no "S" look at all. Looks like a "lowering" exponential trend for any timeframe.
To have a "S" look que should use another regression function, like

That's what I said... the 'S' shape (of slipperyslope, e.g.) is bounded growth, i.e. is convergent. Your function doesn't have a finite limit. It just goes to infinity rather slowly

[dnaleor]

I remember that, late last year, when price exceeded even the loglinear model's predictions, some analysis was posted that suggested a superexponential price function to model BTC price.

that was fun
We would be > 600k by now

edit: just posting it for the lulz:

[Capt Drake]

Very nice work man!!

I'll be watching your future updates on this! 

[Trolololo]

nice charts

will folow your posts from now on

edit: left you a small tip

Thank you!

[superresistant]

Nice graphics and nice work! 
What software did you use?

Excel.
As Rpietila says, you can do amazing things with excel.

Impressive.
Yes, Excel (or equivalent) can do so much things.

EDIT :
I can only agree with the estimate, 1.000 USD by 24-04-2015
But that's only an estimation.

[smooth]

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

10^ln(x) = x^ln(10)

[cbeast]

Let's now see some new analytics using splines and regressive curvilinear functions. I'm so tired of seeing mspaint lines over boring plots. The speculation threads will love these.

[oda.krell]

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

10^ln(x) = x^ln(10)

Thanks. Feel like an idiot for missing that.

Which would make it about quadratic growth. Interesting.

[laurentmt]

In what year does your regression intersect with $1M USD?

I would say for Xmas 2026 

[smooth]

I'm not sure about the exact type of growth of your function. What you seem to be mapping is logarithmic growth (slow) on a log chart (fast). Stripped of its minor constants, your formula is of the form 10^ln(t) for time = t. ln(t) grows extremely slow over time, but the result is used as a positive, growing exponent.

10^ln(x) = x^ln(10)

Thanks. Feel like an idiot for missing that.

Which would make it about quadratic growth. Interesting.

Yes I thought so too. If you buy the Metcalf's Law valuation argument (I don't entirely), that corresponds roughly with linear growth of usage. Which interestingly is what Chris Dixon has said they are seeing in his businesses (mostly Coinbase I think).

[macsga]

Following. Great job indeed. Congrats.

[ssmc2]

This is in my weekly repertoire of threads I look at to give me that warm blanket feeling