Topic: Non-spreadsheet long-term predictions (Read 8962 times)
Any plans to update the model in the near future? Interested to see how it looks now that its been 3 months from the last update.
exocytosis: "This user is currently ignored.: 
* Just for fun -- projected price on 2014-12-31 is 438.
Quoted for future reference. We'll see in a couple of weeks.
interesting... unfortunately, price is still behind 
following
How have I never noticed this post before? Very interesting, will save a check back frequently.
Pretty accurate.
We're floating around 366 and it's predicted 366 for P50
We're floating around 366 and it's predicted 366 for P50
What technical analysis tools do you use? I am curious.
No easy answer to that question. Probably makes more sense to describe my two big meta-strategies, and then fill in some of the details: trend following based on momentum, and mean reversion based on clearly identifiable outliers. Not very original, I know.
For the momentum trades, the basis is usually price (close, high, low, sometimes hl2) in relation to some averages (either simple moving averages, which shouldn't work, but does, or more commonly, averages with some form of exponential smoothing). Plus divergences on the conventional indicators (like MACD or RSI). And finally: volume analysis (in relation to price, and over time). Extremely important factor in this market, in my opinion.
The mean reversion decisions are a bit more complicated, but price in relation to some average is the basis for that as well, though picking up additional clues (like the divergences mentioned above) becomes more important unless I want to enter deeply unprofitable trades.
Trading frequency I aim for is once every few weeks, possibly months. In summary, discretionary swing/position trading, with some amount of algorithmic input and backtesting from experimental methods or indicators.
What technical analysis tools do you use? I am curious.
@Joe200
Good decision, imo (to "fix" the model as using the entire history, and see what you get doing so).
I've said it before (somewhere on page 1 iirc), but your model is one of the more, maybe the most, mathematically mature of the long-term models, if for no other reason that you provide interval estimates. This model, like the others, still suffers from the obvious problem of changing parameters, but then again, the more accurate you'd like to get in your market predictions the narrower your predictive time frame has to get presumably, so maybe that's the trade-off that we have to accept: Your model does make a prediction into far future, but will either have a high error rate at times (using the "median scenario" as a point estimate), or imprecise (using the entire interval range). There are probably more precise, less error prone ways to look at the market, but you'd be happy if you can predict 2 days into the future with them. So, apples and oranges.
Not sure I agree with your assessment that it's all voodoo/cargo cult what technical analysis is doing, but happy to hear we're not disagreeing on the basic premise itself, which is surprisingly common in here: whether prediction (based on past market data) is possible in principle, or whether some absolute interpretation of fundamentals aka "the news" determines price. (I say "surprisingly common", because I always wonder what people that don't believe prediction is possible even do in a speculation forum. Complain about the unpredictability of the markets, I guess)
Good decision, imo (to "fix" the model as using the entire history, and see what you get doing so).
I've said it before (somewhere on page 1 iirc), but your model is one of the more, maybe the most, mathematically mature of the long-term models, if for no other reason that you provide interval estimates. This model, like the others, still suffers from the obvious problem of changing parameters, but then again, the more accurate you'd like to get in your market predictions the narrower your predictive time frame has to get presumably, so maybe that's the trade-off that we have to accept: Your model does make a prediction into far future, but will either have a high error rate at times (using the "median scenario" as a point estimate), or imprecise (using the entire interval range). There are probably more precise, less error prone ways to look at the market, but you'd be happy if you can predict 2 days into the future with them. So, apples and oranges.
Not sure I agree with your assessment that it's all voodoo/cargo cult what technical analysis is doing, but happy to hear we're not disagreeing on the basic premise itself, which is surprisingly common in here: whether prediction (based on past market data) is possible in principle, or whether some absolute interpretation of fundamentals aka "the news" determines price. (I say "surprisingly common", because I always wonder what people that don't believe prediction is possible even do in a speculation forum. Complain about the unpredictability of the markets, I guess
)
Posted an update on the main page.
This is the post from 2014-11-19.
(I am copying the original message to here. This page will have the latest.)
The spreadsheet extrapolation. Many people plot log price versus time, find the best fitting line, and extrapolate it. This is what they get:
R2 = 90%! This model MUST be correct. Add in the bias -- if this model is correct, we will be making 0.57% per day forever. Who doesn't like that.
What others point out in response is that the trend cannot go on forever. Although, even if log price vs. time is an S-shaped curve, we really don't know where we are in that curve. If we near the beginning of that curve, then the linear extrapolation is fine. Or are we further along?
Even if we are near the beginning of the S-curve, there is another issue. OLS assumes that the residuals are independent of each other, which, in a time series, is clearly and completely false. And we should talk about confidence intervals as well, not just a point estimate.
A better model. Here is a very basic model, the assumptions for which are actually not violated.
The difference in the log price, which is approximately the daily percent return, has a Normal distribution with mean mu and standard deviation sigma. Am I saying that this is the "true" correct model? No. This is a useful simplification.
Assuming that mu and sigma could change over time, this model does not take that into account. We would have to decide outside of the model how much data to use to estimate the current mu and sigma.
Let's look at estimates of mu and sigma based on half year and one year chunks of data.
A lot of information here. What do you see? Here is what jumps out at me.
* Yearly chunks of data. This past year had a negative return, for the first time ever. This is disturbing for HODLers.
* Half year chunks of data. This past half year had a negative return. The only other time with a negative return was 2011-05-11 to 2011-11-14. That's when the most giant crash so far happened -- from 2011-06-09 / 29.6 to 2011-11-18 / 2.14, a loss of 92.8%.
* Interestingly, with the current negative return, sigma (volatility) is also small. Also interestingly, during the 2011-05-11 to 2011-11-14 period, volatility did not decrease. What do you think this all means?
We have to think a lot more carefully about how much data to use to make the estimates. The projections into the future are pretty straightforward, if we have good estimates of the parameters. Ideas welcome.
History.
* 2014-05-08
* 2014-06-26
The spreadsheet extrapolation. Many people plot log price versus time, find the best fitting line, and extrapolate it. This is what they get:
Code:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.6131065 0.0434221 -37.15 <2e-16 ***
day 0.0056570 0.0000477 118.60 <2e-16 ***
R-squared: 0.8994
R2 = 90%! This model MUST be correct. Add in the bias -- if this model is correct, we will be making 0.57% per day forever. Who doesn't like that.
What others point out in response is that the trend cannot go on forever. Although, even if log price vs. time is an S-shaped curve, we really don't know where we are in that curve. If we near the beginning of that curve, then the linear extrapolation is fine. Or are we further along?
Even if we are near the beginning of the S-curve, there is another issue. OLS assumes that the residuals are independent of each other, which, in a time series, is clearly and completely false. And we should talk about confidence intervals as well, not just a point estimate.
A better model. Here is a very basic model, the assumptions for which are actually not violated.
Code:
diff log price ~ Normal(mu, sigma)
The difference in the log price, which is approximately the daily percent return, has a Normal distribution with mean mu and standard deviation sigma. Am I saying that this is the "true" correct model? No. This is a useful simplification.
Assuming that mu and sigma could change over time, this model does not take that into account. We would have to decide outside of the model how much data to use to estimate the current mu and sigma.
Let's look at estimates of mu and sigma based on half year and one year chunks of data.
Code:
n.data from to mu sigma z.stat diff.mu diff.sd diff.z
1 115 2010-07-17 2010-11-08 0.0161 0.0854 0.189 NA NA NA
2 183 2010-11-09 2011-05-10 0.0147 0.0722 0.204 -0.00141 -0.0132 0.0149
3 182 2011-05-11 2011-11-14 -0.00349 0.0876 -0.0399 -0.0182 0.0154 -0.244
4 183 2011-11-15 2012-05-15 0.00378 0.0392 0.0963 0.00727 -0.0484 0.136
5 183 2012-05-16 2012-11-14 0.00427 0.0323 0.132 0.000496 -0.00695 0.0361
6 182 2012-11-15 2013-05-15 0.0127 0.0799 0.159 0.00842 0.0476 0.0265
7 183 2013-05-16 2013-11-16 0.00735 0.0372 0.198 -0.00534 -0.0427 0.039
8 182 2013-11-17 2014-05-17 0.000315 0.0507 0.00622 -0.00704 0.0135 -0.192
9 183 2014-05-18 2014-11-19 -0.000951 0.0242 -0.0393 -0.00127 -0.0265 -0.0455
Code:
n.data from to mu sigma z.stat diff.mu diff.sd diff.z
1 115 2010-07-17 2010-11-08 0.0161 0.0854 0.189 NA NA NA
2 365 2010-11-09 2011-11-14 0.00564 0.0808 0.0698 -0.0105 -0.00461 -0.119
3 366 2011-11-15 2012-11-14 0.00402 0.0359 0.112 -0.00162 -0.0449 0.0422
4 365 2012-11-15 2013-11-16 0.01 0.0623 0.161 0.00599 0.0264 0.0487
5 365 2013-11-17 2014-11-19 -0.00032 0.0397 -0.00805 -0.0103 -0.0226 -0.169
A lot of information here. What do you see? Here is what jumps out at me.
* Yearly chunks of data. This past year had a negative return, for the first time ever. This is disturbing for HODLers.
* Half year chunks of data. This past half year had a negative return. The only other time with a negative return was 2011-05-11 to 2011-11-14. That's when the most giant crash so far happened -- from 2011-06-09 / 29.6 to 2011-11-18 / 2.14, a loss of 92.8%.
* Interestingly, with the current negative return, sigma (volatility) is also small. Also interestingly, during the 2011-05-11 to 2011-11-14 period, volatility did not decrease. What do you think this all means?
We have to think a lot more carefully about how much data to use to make the estimates. The projections into the future are pretty straightforward, if we have good estimates of the parameters. Ideas welcome.
History.
* 2014-05-08
* 2014-06-26
Maybe I didn't phrase it very clearly. What I tried to say wasn't that his analysis is biased or subjective, but that the way he is adjusting/refining his model reminds of the path that one takes when attempting to trade the market based on ("traditional") technical analysis. 'Pattern finding', as opposed to the more rigorous, but maybe also rather futile attempt to do purely quantitative forecasting. It's not a black/white distinction, just what his updated model suddenly made me think of.
I am a big believer in the basic axiom of technical analysis, though I think that the actual tools of technical analysis are all voodoo. The axiom is that what people think is "fundamentals" is actually driven by price. "News X just happened, the price should go up, and here it is going up." WRONG. This is your interpretation of News X in a bull market. In a bear market, you would probably not even notice News X. And if you do, you interpret its influence on price differently.
This same thing started happening to me in this thread. My biases came into it. When I believed that the price would recover quickly, I said, let's just use all the data to estimate the parameters. Now, with the longest bear market to date, I am scared. My mind is playing tricks on me. My model seems objective. But how I choose to construct the model is subjective. And my views are influenced by the price. Price action is driving something that's seemingly objective.
As I explained in the last post, I will just use all the data in this thread.
Thanks for the update, Joe200. Pleasure to read, as before.
I notice you're changing the approach a bit: first time, you used all available data for the estimates, now you're using a half year/one year period preceding the time of calculation, and see how the parameters change over time. Correct so far?
Don't get this the wrong way, it's not meant to be a criticism of your attempt to model price, but I do find it interesting that it looks to me like you are getting closer to some of the considerations that drive technical analysts.
What I mean is this: you started (some months ago) by looking at the entire available data for your estimates. Turns out, at any point in time, this can lead to wildly unreliable predictions (especially if the preceding period saw a huge price increase or decrease). Now you're breaking down the data into smaller chunks, and try to see how the parameters change over time. The next logical step seems to be to start varying the history size, and try to see if the parameters change in some systematic way in the past, i.e. if there's some pattern to how they change over time. Sorry to say it, but you're one of us now
I notice you're changing the approach a bit: first time, you used all available data for the estimates, now you're using a half year/one year period preceding the time of calculation, and see how the parameters change over time. Correct so far?
Don't get this the wrong way, it's not meant to be a criticism of your attempt to model price, but I do find it interesting that it looks to me like you are getting closer to some of the considerations that drive technical analysts.
What I mean is this: you started (some months ago) by looking at the entire available data for your estimates. Turns out, at any point in time, this can lead to wildly unreliable predictions (especially if the preceding period saw a huge price increase or decrease). Now you're breaking down the data into smaller chunks, and try to see how the parameters change over time. The next logical step seems to be to start varying the history size, and try to see if the parameters change in some systematic way in the past, i.e. if there's some pattern to how they change over time. Sorry to say it, but you're one of us now
Oda,
You are right.
I always knew that the parameters changing over time could become an issue, I just didn't know how to deal with it, and still don't. When I made my original post, I got lucky -- the parameter estimates using all of the data were very close to the parameter estimates using just the most recent 2 years of data. I waved my hands and pretended like the parameters don't change over time, and gave my predictions.
This time around, we are in the longest bear market ever (https://bitcointalksearch.org/topic/previous-crashes-and-recoveries-676333). The parameter estimates using all the data are quite different from the parameter estimates using the most recent data. This gave me pause.
After thinking about this for a couple of days, here is what I decided. I am not going to develop the One True Model of Bitcoin Price(TM) in one simple post. The original purpose of this thread was simply to explain that the linear extrapolation on the log-price chart that so many people do is complete nonsense, and to give a model that's similar in spirit but that's more sound. The name of the model is the Basic Long-Term Model. Nothing more. This model is indeed an improvement on the log-price chart extrapolation. It might not be a very good model, but that, in a sense, is not the point.
So I've decided that, in this thread, I will just keep using all available data. It's easy to do, easy to explain, and easy to understand. This is not the One True Model of Bitcoin Price(TM). I have other threads with other models. I hope that each one contributes something.
...
At lot of the analysis around here is shaped by personal opinions.Still, I hope he is right!
Maybe I didn't phrase it very clearly. What I tried to say wasn't that his analysis is biased or subjective, but that the way he is adjusting/refining his model reminds of the path that one takes when attempting to trade the market based on ("traditional") technical analysis. 'Pattern finding', as opposed to the more rigorous, but maybe also rather futile attempt to do purely quantitative forecasting. It's not a black/white distinction, just what his updated model suddenly made me think of.
Thanks for the update, Joe200. Pleasure to read, as before.
I notice you're changing the approach a bit: first time, you used all available data for the estimates, now you're using a half year/one year period preceding the time of calculation, and see how the parameters change over time. Correct so far?
Don't get this the wrong way, it's not meant to be a criticism of your attempt to model price, but I do find it interesting that it looks to me like you are getting closer to some of the considerations that drive technical analysts.
What I mean is this: you started (some months ago) by looking at the entire available data for your estimates. Turns out, at any point in time, this can lead to wildly unreliable predictions (especially if the preceding period saw a huge price increase or decrease). Now you're breaking down the data into smaller chunks, and try to see how the parameters change over time. The next logical step seems to be to start varying the history size, and try to see if the parameters change in some systematic way in the past, i.e. if there's some pattern to how they change over time. Sorry to say it, but you're one of us now
At lot of the analysis around here is shaped by personal opinions.I notice you're changing the approach a bit: first time, you used all available data for the estimates, now you're using a half year/one year period preceding the time of calculation, and see how the parameters change over time. Correct so far?
Don't get this the wrong way, it's not meant to be a criticism of your attempt to model price, but I do find it interesting that it looks to me like you are getting closer to some of the considerations that drive technical analysts.
What I mean is this: you started (some months ago) by looking at the entire available data for your estimates. Turns out, at any point in time, this can lead to wildly unreliable predictions (especially if the preceding period saw a huge price increase or decrease). Now you're breaking down the data into smaller chunks, and try to see how the parameters change over time. The next logical step seems to be to start varying the history size, and try to see if the parameters change in some systematic way in the past, i.e. if there's some pattern to how they change over time. Sorry to say it, but you're one of us now
Still, I hope he is right!
Thanks for the update, Joe200. Pleasure to read, as before.
I notice you're changing the approach a bit: first time, you used all available data for the estimates, now you're using a half year/one year period preceding the time of calculation, and see how the parameters change over time. Correct so far?
Don't get this the wrong way, it's not meant to be a criticism of your attempt to model price, but I do find it interesting that it looks to me like you are getting closer to some of the considerations that drive technical analysts.
What I mean is this: you started (some months ago) by looking at the entire available data for your estimates. Turns out, at any point in time, this can lead to wildly unreliable predictions (especially if the preceding period saw a huge price increase or decrease). Now you're breaking down the data into smaller chunks, and try to see how the parameters change over time. The next logical step seems to be to start varying the history size, and try to see if the parameters change in some systematic way in the past, i.e. if there's some pattern to how they change over time. Sorry to say it, but you're one of us now
I notice you're changing the approach a bit: first time, you used all available data for the estimates, now you're using a half year/one year period preceding the time of calculation, and see how the parameters change over time. Correct so far?
Don't get this the wrong way, it's not meant to be a criticism of your attempt to model price, but I do find it interesting that it looks to me like you are getting closer to some of the considerations that drive technical analysts.
What I mean is this: you started (some months ago) by looking at the entire available data for your estimates. Turns out, at any point in time, this can lead to wildly unreliable predictions (especially if the preceding period saw a huge price increase or decrease). Now you're breaking down the data into smaller chunks, and try to see how the parameters change over time. The next logical step seems to be to start varying the history size, and try to see if the parameters change in some systematic way in the past, i.e. if there's some pattern to how they change over time. Sorry to say it, but you're one of us now
Interesting approach and data.
Congratulations!
Congratulations!
See update on the front page.
https://bitcointalksearch.org/topic/non-spreadsheet-long-term-predictions-600802
https://bitcointalksearch.org/topic/non-spreadsheet-long-term-predictions-600802
Just putting the original message here. I will now put the latest on the front page.
Tl;dr. Here are the price predictions for Bitstamp BTC/USD.
p_50 is the median prediction, p_5 is the "pessimistic" prediction, and p_95 is the "optimistic" prediction. In a year, we could reasonably be at 10x where we are right now. Or, we could be still at where we are now. Read on for a discussion.
The spreadsheet extrapolation. Many people plot log price versus time, find the best fitting line, and extrapolate it. This is what they get:
Look at this -- R2 = 90%! We are making 0.6% per day. No problem.
What others point out in response is that the trend cannot go on forever. While the long-term curve could in fact be S-shaped, we could still be in the early part of it. The trend does appear to be increasing (log) linearly. So, in my view, that's not the real issue.
The real issue is that OLS assumes that the residuals are independent of each other, which, in a time series, is clearly and completely false. And we should talk about confidence intervals as well, not just a point estimate.
A better model. Here is a very simple / basic model, the assumptions for which are actually not violated. The difference in the log price, which is approximately the daily percent return, has a Normal distribution with mean mu and standard deviation sigma.
Using all available data, we have
So yes, there has actually been a growth of 0.66% per day. But also look at the standard deviation. CV (the ratio of sigma / mu) is around 10 -- there is a lot of variation.
More estimates. Are these parameters changing with time? Is mu perhaps drifting? Here are the historical values:
After the initial explosion (1.5% per day!), mu has been relatively stable - though it is not in its lower range. Sigma / volatility has declined too. Anyone have any other insights on this?
But maybe the market is changing, which would mean that we should ignore old data. Here are estimates using only a year's worth of data.
In the past year, mu has been really low. CV is the second highest that it's ever been. -- But mu can't go any lower for now, right? Cuz we've bottomed out? Anyone has any thoughts on this table?
Predictions. Predictions using all of the available data are at the top of the post. A year from now, the median prediction is $4,890 per coin. Meaning we could be at 10x of where we are. The pessimistic prediction is $489. I don't see how we just sit here for a year, but I guess it's possible. And the "to the moon" prediction? In 2 years, we could be at $$$ 2 million dollars $$$ per coin. :-) Ladies and gentlemen, hold on to your coinz. :-)
What if the market has changed and we should be ignoring the early days? Interestingly enough, the parameters in the past 2 years are almost the same as the parameters that use all of the data.
And so the prediction using the past 2 years of data is very similar to the prediction that uses all the data.
In a year, we are still at either 10x or, if things go bad, at the same price as now. In 2 years, "to the moon" is $1.4 mil instead of $1.9 mil.
Break-even point. If you buy today and thing go bad, how long will you have to hold to get your fiat back? Here is a prediction using all of the data:
331 days -- less than a year. So keep buying. :-) Buy coins, come back a year later, and you will very likely have made a profit.
Thoughts, comments, suggestions, criticisms are very much appreciated.
Code:
n.fut date p_5 p_50 p_95
1 0 2014-05-08 NA 446 NA
2 1 2014-05-09 403 448 499
3 7 2014-05-15 351 466 620
4 30 2014-06-07 300 542 982
5 91 2014-08-07 282 810 2,330
6 365 2015-05-08 489 4,890 48,800
7 731 2016-05-08 1,500 54,000 1,940,000
p_50 is the median prediction, p_5 is the "pessimistic" prediction, and p_95 is the "optimistic" prediction. In a year, we could reasonably be at 10x where we are right now. Or, we could be still at where we are now. Read on for a discussion.
The spreadsheet extrapolation. Many people plot log price versus time, find the best fitting line, and extrapolate it. This is what they get:
Code:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.817e+00 4.592e-02 -39.57 <2e-16 ***
day 6.062e-03 5.735e-05 105.70 <2e-16 ***
R-squared: 0.8898
Look at this -- R2 = 90%! We are making 0.6% per day. No problem.
What others point out in response is that the trend cannot go on forever. While the long-term curve could in fact be S-shaped, we could still be in the early part of it. The trend does appear to be increasing (log) linearly. So, in my view, that's not the real issue.
The real issue is that OLS assumes that the residuals are independent of each other, which, in a time series, is clearly and completely false. And we should talk about confidence intervals as well, not just a point estimate.
A better model. Here is a very simple / basic model, the assumptions for which are actually not violated.
Code:
diff log price ~ Normal(mu, sigma)
Using all available data, we have
Code:
n.data from to mu sigma cv
1 1,380 2010-07-17 2014-05-08 0.00656 0.0652 9.93
So yes, there has actually been a growth of 0.66% per day. But also look at the standard deviation. CV (the ratio of sigma / mu) is around 10 -- there is a lot of variation.
More estimates. Are these parameters changing with time? Is mu perhaps drifting? Here are the historical values:
Code:
n.data from to mu sigma cv
1 183 2010-07-17 2011-01-16 0.01120 0.0810 7.25
2 365 2010-07-17 2011-07-23 0.01530 0.0834 5.44
3 548 2010-07-17 2012-01-22 0.00881 0.0788 8.95
4 731 2010-07-17 2012-07-23 0.00701 0.0697 9.95
5 913 2010-07-17 2013-01-21 0.00634 0.0638 10.10
6 1,100 2010-07-17 2013-07-23 0.00688 0.0675 9.81
7 1,280 2010-07-17 2014-01-21 0.00759 0.0664 8.75
8 1,380 2010-07-17 2014-05-08 0.00656 0.0652 9.93
After the initial explosion (1.5% per day!), mu has been relatively stable - though it is not in its lower range. Sigma / volatility has declined too. Anyone have any other insights on this?
But maybe the market is changing, which would mean that we should ignore old data. Here are estimates using only a year's worth of data.
Code:
n.data from to mu sigma cv
1 289 2010-07-17 2011-05-02 0.01440 0.0777 5.40
2 365 2010-11-01 2011-11-07 0.00754 0.0820 10.90
3 365 2011-05-03 2012-05-08 0.00120 0.0689 57.30
4 365 2011-11-07 2012-11-06 0.00354 0.0374 10.60
5 365 2012-05-08 2013-05-08 0.00851 0.0608 7.15
6 365 2012-11-06 2013-11-06 0.00866 0.0618 7.14
7 365 2013-05-08 2014-05-08 0.00390 0.0527 13.50
In the past year, mu has been really low. CV is the second highest that it's ever been. -- But mu can't go any lower for now, right? Cuz we've bottomed out? Anyone has any thoughts on this table?
Predictions. Predictions using all of the available data are at the top of the post. A year from now, the median prediction is $4,890 per coin. Meaning we could be at 10x of where we are. The pessimistic prediction is $489. I don't see how we just sit here for a year, but I guess it's possible. And the "to the moon" prediction? In 2 years, we could be at $$$ 2 million dollars $$$ per coin. :-) Ladies and gentlemen, hold on to your coinz. :-)
What if the market has changed and we should be ignoring the early days? Interestingly enough, the parameters in the past 2 years are almost the same as the parameters that use all of the data.
Code:
n.data from to mu sigma cv
1 731 2012-05-07 2014-05-08 0.00612 0.0569 9.3
And so the prediction using the past 2 years of data is very similar to the prediction that uses all the data.
Code:
n.fut date p_5 p_50 p_95
1 0 2014-05-08 NA 446 NA
2 1 2014-05-09 408 448 492
3 7 2014-05-15 363 465 596
4 30 2014-06-07 317 535 903
5 91 2014-08-07 302 778 2,000
6 365 2015-05-08 466 4,160 37,100
7 731 2016-05-08 1,090 39,100 1,400,000
In a year, we are still at either 10x or, if things go bad, at the same price as now. In 2 years, "to the moon" is $1.4 mil instead of $1.9 mil.
Break-even point. If you buy today and thing go bad, how long will you have to hold to get your fiat back? Here is a prediction using all of the data:
Code:
n.fut date p_5 p_50 p_95
1 331 2015-04-04 446 3,910 34,300
331 days -- less than a year. So keep buying. :-) Buy coins, come back a year later, and you will very likely have made a profit.
Thoughts, comments, suggestions, criticisms are very much appreciated.
Bump for awesomeness 
if BitCoin will be 1000 USD in 2016, is really good time to buy.
i believe that, if you are looking at 1-2 year terms, its a no-brainer that you will atleast double your earnings.
problem is that alot of daytraders invaded bitcoin trading, keeping their profits in fiat, and reducing the money inflow.
if BitCoin will be 1000 USD in 2016, is really good time to buy.
tl;dr. Doing well so far. "Interesting times" possible in late January.
So far. How is this very simplistic model doing so far? Here is the projection of the model using the data up to 2014-05-08, which is when I posted the original projection.
You will note that this is slightly different than the original projection. The reason is that the price that I originally used on 2014-05-08 was not the correct price for that day, but the price at the time of the writing, which was slightly different.
To make things more interesting, I am showing more percentiles.
Under the original prediction, today, a full 47 days later, the median predicted price is 604. The 50% CI is 445 to 821. The actual price as I am writing this is 568. Well within the 50% CI, and pretty close to the median prediction. Not bad, if I do say so myself. ;-)
Updated predictions. Same very simplistic model using the most current data.
mu, sigma, and cv are all down. Meaning, both expected return and volatility have adjusted down. These are very small changes, which is what you would expect since we only added a few new data points.
Using the median outlook (p_50), we should finally break through 1k by late October. By late January, we should be at 2,270. According to my Peak/trough model (PTM), once we reach that price level, "the moon" (the next peak) should be less than a month away. According to the PTM prediction, which I have not updated recently, the peak should happen in mid-January. If I did update the PTM prediction, that would push the peak back -- how far I don't know, but at least to late January.
In other words, the two models are making a similar prediction. Come late January, watch out, we might be blasting off (this model) or already on the moon (PTM).
This assumes that the median outlook holds. Under a "poor" outlook (p_25), come late January, we will "only" be breaking above 1k. Not the moon, not the launchpad, but still a lot of excitement.
About intervals. Look at the predictions again. Yes, these intervals are huge. I like to think of these as "honest intervals" (conditional on the model being a decent approximation of reality, which is a stretch). The intervals reflect the amount of uncertainty. There is a lot of uncertainty, especially the further out you go. These intervals help highlight that fact.
So far. How is this very simplistic model doing so far? Here is the projection of the model using the data up to 2014-05-08, which is when I posted the original projection.
Code:
n.data from to mu sigma cv
1 1,380 2010-07-17 2014-05-08 0.00656 0.0652 9.93
n.fut date p_5 p_25 p_50 p_75 p_95
1 0 2014-05-08 NA NA 444 NA NA
2 1 2014-05-09 401 428 447 467 497
3 7 2014-05-15 350 414 465 522 617
4 30 2014-06-07 299 424 540 689 978
5 47 2014-06-24 286 445 604 821 1,280
6 61 2014-07-08 282 466 662 940 1,560
You will note that this is slightly different than the original projection. The reason is that the price that I originally used on 2014-05-08 was not the correct price for that day, but the price at the time of the writing, which was slightly different.
To make things more interesting, I am showing more percentiles.
Under the original prediction, today, a full 47 days later, the median predicted price is 604. The 50% CI is 445 to 821. The actual price as I am writing this is 568. Well within the 50% CI, and pretty close to the median prediction. Not bad, if I do say so myself. ;-)
Updated predictions. Same very simplistic model using the most current data.
Code:
n.data from to mu sigma cv
1 1,430 2010-07-17 2014-06-26 0.00651 0.0642 9.87
n.fut date p_5 p_25 p_50 p_75 p_95
1 0 2014-06-26 NA NA 568 NA NA
2 1 2014-06-27 514 547 571 597 635
3 7 2014-07-03 449 530 594 666 786
4 30 2014-07-26 384 543 690 877 1,240
5 61 2014-08-26 363 597 844 1,190 1,960
6 91 2014-09-25 363 670 1,030 1,570 2,900
7 122 2014-10-26 372 763 1,260 2,070 4,240
8 152 2014-11-25 388 870 1,530 2,680 6,010
9 183 2014-12-26 409 1,000 1,870 3,480 8,520
10 188 2014-12-31 413 1,030 1,930 3,630 9,010
11 213 2015-01-25 435 1,150 2,270 4,470 11,900
12 244 2015-02-25 466 1,340 2,780 5,780 16,600
13 274 2015-03-27 500 1,540 3,380 7,380 22,800
14 304 2015-04-26 540 1,790 4,100 9,430 31,200
15 335 2015-05-27 586 2,080 5,020 12,100 43,000
16 365 2015-06-26 636 2,410 6,100 15,400 58,600
17 731 2016-06-26 1,970 15,600 66,000 279,000 2,210,000
mu, sigma, and cv are all down. Meaning, both expected return and volatility have adjusted down. These are very small changes, which is what you would expect since we only added a few new data points.
Using the median outlook (p_50), we should finally break through 1k by late October. By late January, we should be at 2,270. According to my Peak/trough model (PTM), once we reach that price level, "the moon" (the next peak) should be less than a month away. According to the PTM prediction, which I have not updated recently, the peak should happen in mid-January. If I did update the PTM prediction, that would push the peak back -- how far I don't know, but at least to late January.
In other words, the two models are making a similar prediction. Come late January, watch out, we might be blasting off (this model) or already on the moon (PTM).
This assumes that the median outlook holds. Under a "poor" outlook (p_25), come late January, we will "only" be breaking above 1k. Not the moon, not the launchpad, but still a lot of excitement.
About intervals. Look at the predictions again. Yes, these intervals are huge. I like to think of these as "honest intervals" (conditional on the model being a decent approximation of reality, which is a stretch). The intervals reflect the amount of uncertainty. There is a lot of uncertainty, especially the further out you go. These intervals help highlight that fact.
That P_50 has me hot and bothered.. let me take you out OP hehehe.
How about basing the predictions on real world money supply? Curiously, your answers are not that different!See https://bitcointalksearch.org/topic/if-bitcoin-became-the-world-reserve-currency-646186
Hum.. what?
Are you trying to get me all excited as well?
That P_50 has me hot and bothered.. let me take you out OP hehehe.
How about basing the predictions on real world money supply? Curiously, your answers are not that different!See https://bitcointalksearch.org/topic/if-bitcoin-became-the-world-reserve-currency-646186
That P_50 has me hot and bothered.. let me take you out OP hehehe.
Of all the dubious log linear extrapolation models, the least dubious one.
(yes, I mean that as a compliment.)
(yes, I mean that as a compliment.)
For sure.
However I say chart-based extrapolation still doesn't work longterm. Extrapolation can't predict major mood changes of market participants or sudden events. Whatever type of extrapolation you use, it is always just projecting the main trend into the future.
Such methods may work quite a long time, but suddenly they will fail. For better predictions you would have to monitor constantly the fundamentals that drive market mechanics (for example adoption rate, adoption pool (people likely to become adopters), transaction volume growth, businesses accepting btc).
Which is what gbianchi is doing in this thread...
https://bitcointalksearch.org/topic/18-mar-data-a-bitcoin-price-theory-441336
... modeling network growth (which is then related to price) based on zero balance addresses.
However, Joe200's model is mathematically more mature. How about a collaboration?
Of all the dubious log linear extrapolation models, the least dubious one.
(yes, I mean that as a compliment.)
(yes, I mean that as a compliment.)
For sure.
However I say chart-based extrapolation still doesn't work longterm. Extrapolation can't predict major mood changes of market participants or sudden events. Whatever type of extrapolation you use, it is always just projecting the main trend into the future.
Such methods may work quite a long time, but suddenly they will fail. For better predictions you would have to monitor constantly the fundamentals that drive market mechanics (for example adoption rate, adoption pool (people likely to become adopters), transaction volume growth, businesses accepting btc).
Of all the dubious log linear extrapolation models, the least dubious one.
(yes, I mean that as a compliment.)
(yes, I mean that as a compliment.)
This post deserves more visibility.
Good and realistic predictions and if your predictions are correct then I'll be one happy man.
2016-05-08 p_95 me want 
I was reading a few old threads (2012 ish i think) where price was 10-30. People said 1k would happen in 2016. No one mentioned 100 (which came shortly after). 1k happened 2013. Many people say 1-8k 2015. Not sure, lets see what happens 2015-2016.
We don't even know what surprises are in store for last half 2014 even!
Interesting. Going to look into this when I have time.
2016-05-08 p_95 me want
I was reading a few old threads (2012 ish i think) where price was 10-30. People said 1k would happen in 2016. No one mentioned 100 (which came shortly after). 1k happened 2013. Many people say 1-8k 2015. Not sure, lets see what happens 2015-2016.
100 and 1K were both in 2013, yes?
2016-05-08 p_95 me want
I was reading a few old threads (2012 ish i think) where price was 10-30. People said 1k would happen in 2016. No one mentioned 100 (which came shortly after). 1k happened 2013. Many people say 1-8k 2015. Not sure, lets see what happens 2015-2016.
2016-05-08 p_95 me want
Great post and good math. The only thing I want to add to get this more "visibility" is that you should actually add some visual charts (graphs) to support your predictions
Cheers for the prediction and explanations. Thanks again for post - Good effort!
This post deserves more visibility
Outstanding charting and mathematics. Thanks!
Great estimations.
This post deserves more visibility
sweet! could be handy
Cheers for the prediction and explanations. I currently have a large big order and waiting for the price to drop, but I hope your models will display a degree of accuracy and we hit $4890 this time next year.
Thanks again for post - Good effort!
Thanks again for post - Good effort!
Nice, Joe!
Latest update: 2014-11-22. See below for history.
The spreadsheet extrapolation. Many people plot log price versus time, find the best fitting line, and extrapolate it. This is what they get:
R2 = 90%! This model MUST be correct. Add in the bias -- if this model is correct, we will be making 0.56% per day forever, compounded. Who doesn't like that.
What others point out in response is that the trend cannot go on forever. Although, even if log price vs. time is an S-shaped curve, we really don't know where we are in that curve. If we are near the beginning of that curve, then the linear extrapolation is fine. Or are we further along?
Even if we are near the beginning of the S-curve, there is another issue. OLS assumes that the residuals are independent of each other, which, in a time series, is clearly and completely false. And we should talk about confidence intervals as well, not just a point estimate.
A better model. Here is a very basic model, the assumptions for which are actually not violated. I call it the Basic Long-Term Model (BLTM).
The difference in the log price, which is approximately the daily percent return, has a Normal distribution with mean mu and standard deviation sigma. Am I saying that this is the "true" correct model? No. This is a useful simplification and an improvement on the log price chart extrapolation. It's easy to perform these calculations, easy to explain, and easy to understand.
The model does not take into account the fact that the model parameters -- mu and sigma -- cound change over time. That is simply outside the scope of this basic model. I am using all available data to estimate the parameters.
Predictions. Here are the parameter estimates and the prediction of this simplistic model.
* In agreement with the log price chart extrapolation, overall, bitcoin has been making 0.56% per day.
* According to the median scenario (p_50), we will hit 1,000 again sometime in early summer 2015.
* According to the pessimistic scenario (p_5), we won't get back to 1,000 even in two years.
* According to the optimistic scenario (p_95), we will break 10,000 by early fall 2015.
* Just for fun -- projected price on 2014-12-31 is 438.
Break-even point. If you buy today and thing go bad, how long will you have to hold to get your fiat back?
388 days.
Comments?
History.
* 2014-05-08
* 2014-06-26
* 2014-11-19
The spreadsheet extrapolation. Many people plot log price versus time, find the best fitting line, and extrapolate it. This is what they get:
Code:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.615e+00 4.340e-02 -37.2 <2e-16 ***
day 5.618e-03 4.729e-05 118.8 <2e-16 ***
R-squared: 0.8995
R2 = 90%! This model MUST be correct. Add in the bias -- if this model is correct, we will be making 0.56% per day forever, compounded. Who doesn't like that.
What others point out in response is that the trend cannot go on forever. Although, even if log price vs. time is an S-shaped curve, we really don't know where we are in that curve. If we are near the beginning of that curve, then the linear extrapolation is fine. Or are we further along?
Even if we are near the beginning of the S-curve, there is another issue. OLS assumes that the residuals are independent of each other, which, in a time series, is clearly and completely false. And we should talk about confidence intervals as well, not just a point estimate.
A better model. Here is a very basic model, the assumptions for which are actually not violated. I call it the Basic Long-Term Model (BLTM).
Code:
diff log price ~ Normal(mu, sigma)
The difference in the log price, which is approximately the daily percent return, has a Normal distribution with mean mu and standard deviation sigma. Am I saying that this is the "true" correct model? No. This is a useful simplification and an improvement on the log price chart extrapolation. It's easy to perform these calculations, easy to explain, and easy to understand.
The model does not take into account the fact that the model parameters -- mu and sigma -- cound change over time. That is simply outside the scope of this basic model. I am using all available data to estimate the parameters.
Predictions. Here are the parameter estimates and the prediction of this simplistic model.
Code:
n.data from to mu sigma z.stat
1 1,579 2010-07-17 2014-11-22 0.00561 0.0602 0.0932
Code:
n.fut date p_5 p_25 p_50 p_75 p_95
1 0 2014-11-22 NA NA 352 NA NA
2 1 2014-11-23 321 340 354 369 391
3 7 2014-11-29 282 329 366 408 476
4 30 2014-12-22 241 333 417 522 720
5 39 2014-12-31 234 339 438 567 820
6 61 2015-01-22 225 359 496 685 1,090
7 91 2015-02-21 222 394 587 874 1,550
8 122 2015-03-24 224 438 698 1,110 2,170
9 152 2015-04-23 230 489 826 1,400 2,970
10 183 2015-05-24 239 550 983 1,760 4,050
11 213 2015-06-23 250 619 1,160 2,190 5,430
12 244 2015-07-24 263 700 1,380 2,740 7,300
13 274 2015-08-23 278 791 1,640 3,390 9,670
14 304 2015-09-22 294 895 1,940 4,200 12,800
15 335 2015-10-23 314 1,020 2,310 5,230 17,000
16 365 2015-11-22 335 1,150 2,730 6,460 22,300
17 404 2015-12-31 365 1,360 3,400 8,480 31,600
18 731 2016-11-22 835 5,640 21,300 80,300 543,000
* In agreement with the log price chart extrapolation, overall, bitcoin has been making 0.56% per day.
* According to the median scenario (p_50), we will hit 1,000 again sometime in early summer 2015.
* According to the pessimistic scenario (p_5), we won't get back to 1,000 even in two years.
* According to the optimistic scenario (p_95), we will break 10,000 by early fall 2015.
* Just for fun -- projected price on 2014-12-31 is 438.
Break-even point. If you buy today and thing go bad, how long will you have to hold to get your fiat back?
Code:
n.fut date p_5 p_25 p_50 p_75 p_95
1 388 2015-12-15 352 1,270 3,110 7,580 27,400
388 days.
Comments?
History.
* 2014-05-08
* 2014-06-26
* 2014-11-19
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