The sigmoid or "S-curve" is the tanh (hyperbolic tangent) function shifted and scaled. Tanh has asymptotes at -1 and 1. Shrink it by half and move it up a little, and you have the logistic function (asymptotes at 0 and 1).
On the linear scale, the logistic (sigmoid) function has an inflection point and asymptotes.
Charted on a log scale, the logistic function doesn't have an inflection point. It has an upper asymptote, but no lower asymptote.
Here is what it looks like
https://www.wolframalpha.com/input/?i=y%3Dlog(1%2F(1%2Be%5E(-x))),-10%3C%3Dx%3C%3D10,-10%3C%3Dy%3C%3D1&x=11&y=7
As you can see, sigmoid is bounded above. This logistic function doesn't look like a very good fit for bitcoin's past or future, what we think of it. It doesn't seem to work with the real numbers.
Modeling the log of the price as a square root function of time, or to put it anther way, modeling the price as an exponential function of the square root of time, implies endless increase. Most likely the model will have to be adjusted, it might even fail completely, but I don't intend to use ratiocination. The empirical approach works much better.
Topic: Abstract Analysis - page 2. (Read 298 times)
The problem with this kind of approach is it places too much emphasis on the long term logarithmic trend. If Bitcoin adoption acts like a technological S-curve, any price projections derived from this will be too low by orders of magnitude.
My personal belief is we are heading towards a major inflection point in the long term chart. Maybe we have another bubble or two left like 2011, 2013, and 2017.....but the pattern is becoming too obvious. It's going to get front run. The log trend is either going to massively accelerate or fail in the coming years.
Likely sooner than that. Historically, Bitcoin never crosses below the previous cycle's ATH. So after we make a new ATH (probably in Q4 this year) I'd consider $20K the lowest possible bottom target in the next bear market. (Unless of course, the historic log trend fails)
My personal belief is we are heading towards a major inflection point in the long term chart. Maybe we have another bubble or two left like 2011, 2013, and 2017.....but the pattern is becoming too obvious. It's going to get front run. The log trend is either going to massively accelerate or fail in the coming years.
So after September 2020 we have lost the possibility to grab dem cheap $10k BTC
Likely sooner than that. Historically, Bitcoin never crosses below the previous cycle's ATH. So after we make a new ATH (probably in Q4 this year) I'd consider $20K the lowest possible bottom target in the next bear market. (Unless of course, the historic log trend fails)
Could you add a max fit parabola just to see where we could be headed?
Even if you knew we were going to max out at 1300~1400 days ahead, like before, you would still have to know when it's going to happen in order to predict the dollar amount.
You can use this chart to look at some possibilities:
If the timing of tops continues to follow on the halvings at even intervals, we might top out at say q4 2021.
So you would take some date in q4 2021, add 1300 or 1400 days, and calculate the value of the parabola (actually as a function of time, a square root function).
The equation for that is
log of price = 0.09348075*sqrt(d)-1.64982665
where d is the number of days elapsed since Sept 8, 2010.
The bash script has some lines in it that calculate days elapsed, you could edit the script to make it so you can input your own arbitrary date and then echo the calculated result. Or you can use a website that calculates days between two dates, like this one https://planetcalc.com/274/
That should be enough info for you to work out the answer to question you asked about the next top.
You could contribute to the thread by letting us know what you find.
So after September 2020 we have lost the possibility to grab dem cheap $10k BTC 
And as I can see bitcoin peaks one digit above the line in it's fluctuation. So $100k is possible however a crash back to $10k is also possible in the next bear market.
Could you add a max fit parabola just to see where we could be headed?
And as I can see bitcoin peaks one digit above the line in it's fluctuation. So $100k is possible however a crash back to $10k is also possible in the next bear market.
Could you add a max fit parabola just to see where we could be headed?
It seems to fit with the 100k scenario.
If bitcoin reaches 100k at the end of 2021, a crash would result in something between 10k and 20k, and the consequent bear market would be in the five digits area, instead of four.
If bitcoin reaches 100k at the end of 2021, a crash would result in something between 10k and 20k, and the consequent bear market would be in the five digits area, instead of four.
The equation for days ahead is 114.43413*(p+1.64983)^2 - d
where p is the log of the price and d is days elapsed since Sept 8, 2010
You can get days elapsed from this website or many others https://planetcalc.com/274/
If you use linux, the bash script in the OP will query the Bitstamp API for the current price, calculate and print the days ahead.
where p is the log of the price and d is days elapsed since Sept 8, 2010
You can get days elapsed from this website or many others https://planetcalc.com/274/
If you use linux, the bash script in the OP will query the Bitstamp API for the current price, calculate and print the days ahead.
The chart below shows a sideways parabola fitted to bitcoin price minima on the log chart. This curve hits ten thousand dollars in September 2020.
The next chart shows how long the parabola takes to catch up to the current price (or any price you choose, as far back as January 2011). You can visualize it, on the first chart, as stretching a horizontal line from a point on the price chart until it intersects the parabola. Today is August 18, 2019, bitcoin’s price is $10,370 and the equation this spreadsheet uses shows 406 days ahead (September 27, 2020).
This bash script will do the calculations
The next chart shows how long the parabola takes to catch up to the current price (or any price you choose, as far back as January 2011). You can visualize it, on the first chart, as stretching a horizontal line from a point on the price chart until it intersects the parabola. Today is August 18, 2019, bitcoin’s price is $10,370 and the equation this spreadsheet uses shows 406 days ahead (September 27, 2020).
This bash script will do the calculations
Code:
#!/bin/bash
read -p “refresh? (y/n) ” answer
while true; do
date –iso-8601
year=$(date +”%Y”)
month=$(expr $(date “+%m”) + 0)
day=$(expr $(date “+%d”) + 0)
#calculate variables for Julian day number
a=$(((14 – month)/12))
y=$((year + 4800 – a))
m=$((month + 12*a – 3))
#calculate Julian day number
jdn=$((day + (153*m+2)/5 + 365*y + y/4 – 32083))
#Sept 8, 2010 jdn=2455461
#d = days elapsed since Sept 8, 2010
d=$((jdn – 2455461))
bid=$(curl -s “https://www.bitstamp.net/api/ticker/” | jq -r “.bid”)
ask=$(curl -s “https://www.bitstamp.net/api/ticker/” | jq -r “.ask”)
#p is midmarket price to 6 decimals
p=$(bc -l <<< “scale=6; ($bid+$ask)/2”)
lnp=$(bc -l <<< “scale=6; l($p)”)
logp=$(bc -l <<< “scale=6; $lnp/2.302585”)
#calculate days ahead
dhed=$(bc -l <<< “scale=6; 114.434128*($logp+1.649827)*($logp+1.649827)-($d)”)
#shift decimal point in preparation for truncating extraneous figures
price1=$(bc -l <<< “scale=6; $p*100”)
#converting to integer truncates extra figures
price2=${price1%.*}
#shift decimal point back
price=$(bc -l <<< “scale=2; $price2/100”)
echo “current price”
echo $price
echo “days ahead”
echo ${dhed%.*}
#calculate root trend and price multiple
root=$(bc -l <<< “scale=8; e(2.30258509*(0.09348075*sqrt($d)-1.64982665))”)
mult1=$(bc -l <<< “scale=8; 100*$price/$root”)
mult=$(bc -l <<< “scale=2; ${mult1%.*}/100”)
echo “price multiple”
echo “$mult”
sleep 15s
if [[ $answer == y ]]; then
continue
else [[ $answer == n ]]
break
fi
done
read -p “refresh? (y/n) ” answer
while true; do
date –iso-8601
year=$(date +”%Y”)
month=$(expr $(date “+%m”) + 0)
day=$(expr $(date “+%d”) + 0)
#calculate variables for Julian day number
a=$(((14 – month)/12))
y=$((year + 4800 – a))
m=$((month + 12*a – 3))
#calculate Julian day number
jdn=$((day + (153*m+2)/5 + 365*y + y/4 – 32083))
#Sept 8, 2010 jdn=2455461
#d = days elapsed since Sept 8, 2010
d=$((jdn – 2455461))
bid=$(curl -s “https://www.bitstamp.net/api/ticker/” | jq -r “.bid”)
ask=$(curl -s “https://www.bitstamp.net/api/ticker/” | jq -r “.ask”)
#p is midmarket price to 6 decimals
p=$(bc -l <<< “scale=6; ($bid+$ask)/2”)
lnp=$(bc -l <<< “scale=6; l($p)”)
logp=$(bc -l <<< “scale=6; $lnp/2.302585”)
#calculate days ahead
dhed=$(bc -l <<< “scale=6; 114.434128*($logp+1.649827)*($logp+1.649827)-($d)”)
#shift decimal point in preparation for truncating extraneous figures
price1=$(bc -l <<< “scale=6; $p*100”)
#converting to integer truncates extra figures
price2=${price1%.*}
#shift decimal point back
price=$(bc -l <<< “scale=2; $price2/100”)
echo “current price”
echo $price
echo “days ahead”
echo ${dhed%.*}
#calculate root trend and price multiple
root=$(bc -l <<< “scale=8; e(2.30258509*(0.09348075*sqrt($d)-1.64982665))”)
mult1=$(bc -l <<< “scale=8; 100*$price/$root”)
mult=$(bc -l <<< “scale=2; ${mult1%.*}/100”)
echo “price multiple”
echo “$mult”
sleep 15s
if [[ $answer == y ]]; then
continue
else [[ $answer == n ]]
break
fi
done
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