I have a Pandas Series that contains the price evolution of a product (my country has high inflation), or say, the amount of coronavirus infected people in a certain country. The values in both of these datasets grows exponentially; that means that if you had something like [3, NaN, 27] you'd want to interpolate so that the missing value is filled with 9 in this case. I checked the interpolation method in the Pandas documentation but unless I missed something, I didn't find anything about this type of interpolation.
I can do it manually, you just take the geometric mean, or in the case of more values, get the average growth rate by doing (final value/initial value)^(1/distance between them) and then multiply accordingly. But there's a lot of values to fill in in my Series, so how do I do this automatically? I guess I'm missing something since this seems to be something very basic.
You could take the logarithm of your series, interpolate lineraly and then transform it back to your exponential scale.
import pandas as pd
import numpy as np
arr = np.exp(np.arange(1,10))
arr = pd.Series(arr)
arr[3] = None
0 2.718282
1 7.389056
2 20.085537
3 NaN
4 148.413159
5 403.428793
6 1096.633158
7 2980.957987
8 8103.083928
dtype: float64
arr = np.log(arr) # Transform according to assumed process.
arr = arr.interpolate('linear') # Interpolate.
np.exp(arr) # Invert previous transformation.
0 2.718282
1 7.389056
2 20.085537
3 54.598150
4 148.413159
5 403.428793
6 1096.633158
7 2980.957987
8 8103.083928
dtype: float64