log-regression.py

# Licensed under the MIT License. See comment below for full licence information.

import pandas as pd
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

## data processing
df = pd.read_csv("data.csv")
df = df[ df['Value'] > 0]
df = df.iloc[::-1]
dates = pd.to_datetime(df['Date'])

## logarithmic function
def func(x, p1,p2):
  return p1*np.log(x)+p2

## fitting data
ydata = np.log(df['Value'])
xdata = [x + 1 for x in range(len(df))]
popt, pcov = curve_fit(func, xdata, ydata,p0=(3.0,-10))

fittedYdata = func(np.array([x for x in range(len(df))]),popt[0],popt[1])
plt.style.use('dark_background')

for i in range(-3,5):
  #plt.plot(dates,np.exp(fittedYdata+i))
  plt.fill_between(dates, np.exp(fittedYdata + i - 1), np.exp(fittedYdata +i), alpha = 0.4)

plt.semilogy(dates,df['Value'])
plt.ylim(bottom = 1)
#plt.show()
plt.savefig("log-regression.png")

Copyright (c) 2020 Chad Thackray

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Here is some sample data you can use. Save it as data.csv in the same folder as the code

Date,Value
2020-12-26,23715.53
2020-12-25,23253.37
2020-12-24,23824.99
2020-12-23,22745.48
2020-12-22,23490.58
2020-12-21,23869.92
2020-12-20,23150.79
2020-12-19,22847.46
2020-12-18,21379.48
2020-12-17,19439.75
2020-12-16,19276.59
2020-12-15,19164.48
2020-12-14,18803.44
2020-12-13,18029.36
2020-12-12,18247.76
2020-12-11,18554.15
2020-12-10,18318.87
2020-12-09,19181.41
2020-12-08,19377.66
2020-12-07,19155.06
2020-12-06,18670.49
2020-12-05,19454.54
2020-12-04,19226.97
2020-12-03,18792.52
2020-12-02,19709.73
2020-12-01,18191.6
2020-11-30,17732.42
2020-11-29,17138.87
2020-11-28,17151.44
2020-11-27,18739.8
2020-11-26,19172.52
2020-11-25,18398.91
2020-11-24,18422.28
2020-11-23,18699.75
2020-11-22,18687.45
2020-11-21,17820.57
2020-11-20,17798.45
2020-11-19,17679.72
2020-11-18,16725.15
2020-11-17,15968.16
2020-11-16,16091.07
2020-11-15,16339.33
2020-11-14,16295.57
2020-11-13,15708.65
2020-11-12,15317.04
2020-11-11,15328.53