scipy.optimize.curve_fit doesn't fit

Question

I want to use curve_fit to do exponential regression, so I can calculate the yearly growth rate of my data.

x is the year, y is assets. If it could fit, the growth-rate should be exp(b) - 1. But it returns (1.0, 1.0, 1.0) as popt.

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

df = pd.DataFrame([
    [2011, 255],
    [2012, 349],
    [2013, 449],
    [2014, 554],
    [2015, 658]
], columns=['x', 'y'])

def func(x, a, b, c):
    return a * np.exp(b * x + c)

popt, pcov = curve_fit(func, df['x'], df['y'])
print('popt', popt)

df['y1'] = func(df['x'], *popt)
print('df\n', df)

plt.plot(df['x'], df['y'])
plt.plot(df['x'], df['y1'], 'g--',
            label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
plt.xlabel('x')
plt.xlabel('y')
plt.legend()
plt.show()

Output:

popt [1.0 1.0 1.0]
df
       x    y   y1
0  2011  255  inf
1  2012  349  inf
2  2013  449  inf
3  2014  554  inf
4  2015  658  inf

If I change x to [1, 2, 3, 4, 5], it could fit.

Answer 1

You are encountering an overflow, since your x values are just too large to fit np.exp(x) into a 64 bit floating point number, see np.exp(2015). One way to handle this, is to fit the function g(x) = func(x-2011) instead:

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

x = np.array([2011, 2012, 2013, 2014, 2015])
y = np.array([255, 349, 449, 554, 658])

def func(x, a, b, c):
    return a * np.exp(b * x + c)

def g(x, a, b, c): 
    return func(x-2011, a, b, c)

popt, pcov = curve_fit(g, x, y)
plt.plot(x, g(x, *popt))
plt.show()