How to calculate percentage when old value is ZERO

Question

I need the logic for the following situation. I am clueless in doing this.

Consider for January I have 10$ revenue and f

Answer 1

How to deal with Zeros when calculating percentage changes is the researcher's call and requires some domain expertise. If the researcher believes that it would not be distorting the data, s/he may simply add a very small constant to all values to get rid of all zeros. In financial series, when dealing with trading volume, for example, we may not want to do this because trading volume = 0 just means that: the asset did not trade at all. The meaning of volume = 0 may be very different from volume = 0.00000000001. This is my preferred strategy in cases whereby I can not logically add a small constant to all values. Consider the percentage change formula ((New-Old)/Old) *100. If New = 0, then percentage change would be -100%. This number indeed makes financial sense as long as it is the minimum percentage change in the series (This is indeed guaranteed to be the minimum percentage change in the series). Why? Because it shows that trading volume experiences maximum possible decrease, which is going from any number to 0, -100%. So, I'll be fine with this value being in my percentage change series. If I normalize that series, then even better since this (possibly) relatively big number in absolute value will be analyzed on the same scale as other variables are. Now, what if the Old value = 0. That's a trickier case. Percentage change due to going from 0 to 1 will be equal to that due to going from 0 to a million: infinity. The fact that we call both "infinity" percentage change is problematic. In this case, I would set the infinities equal to np.nan and interpolate them.

The following graph shows what I discussed above. Starting from series 1, we get series 4, which is ready to be analyzed, with no Inf or NaNs.

One more thing: a lot of the time, the reason for calculating percentage change is to stationarize the data. So, if your original series contains zero and you wish to convert it to percentage change to achieve stationarity, first make sure it is not already stationary. Because if it is, you don't have to calculate percentage change. The point is that series that take the value of 0 a lot (the problem OP has) are very likely to be already stationary, for example the volume series I considered above. Imagine a series oscillating above and below zero, thus hitting 0 at times. Such a series is very likely already stationary.