I have asked this on SO but it has not been well accepted because it seems to be more about data science than programming. Let's say I have a set of data (x=times,y=observation) that have gaps in time. Whatever is their trend, let's assume it linear for this discussion. The actual data do not have a linear trend, and the gaps are more than one, but for the sake of simplicity I would like to deal with a general example that I can understand and then extend to a more specific case. During the gap in time, there is a decay that makes data deviate from the purely linear trend, until observations start again and the linear trend is recovered. I want to model the decay as part of the function.

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

def f(x, A, B, decay):
    return A*x + B + decay

x=[1,2,3, 12,13,14]
y=[2,4,6, 5, 7, 9]
popt, pcov = curve_fit(f, x, y) 

figure = plt.figure(figsize=(5.15, 5.15))
plot = plt.subplot(111)
ax1 = plt.gca()


enter image description here

How do I model the decay variable as part of the function and obtain its best-fit value, let's say in the case where the decay is linear or quadratic? How do I plot the whole function ? I have read something about imputing but I it is the first time I read about it and I am not even sure that is what makes my day.

  • $\begingroup$ Imputation is the process of replacing missing values with some computed values, this can be done in different ways with forward-fill, nearest, linear being some of the more common ways. As for how to model it, that would depend on a lot of factors. Does this decay occur with any regularity? $\endgroup$
    – Shaido
    Apr 29 '20 at 6:00

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