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We have annual reports for company's revenue and can calculate annual growth as $yg = {y_{i+1} \over y_i}$.

And then we can calculate the average monthly growth as $mg = ({y_{i+1} \over y_i})^{1 \over 12}$.

So for reports 2000-12 $1m and 2001-12 $2m the average monthly growth would be 1.06.

But how calculate monthly growth when the revenue became negative?

For reports 2000-12 revenue = $1m and 2001-12 revenue = $-1m?

P.S.

I need it for simple prediction. For example 2000-12 $1m and 2001-12 $2m the revenue in 2002-02 could be predicted as $2 \times 1.06^2 = 2.25$

Alex Craft
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1 Answers1

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An example for negative growth rate: $y_0=100, y_1=80$

The growth rate from $t=0$ to $t=1$ is $g_{01}=\frac{80}{100}-1=0.8-1=-0.2$

So you can use the formula for growth rate no matter whether the growth rate is positive or negative:

$$g_{t,t+1}=\frac{y_{t+1}}{y_t}-1$$

Btw, the growth factor $1+g_{01}$ is still positive $1-0.2=0.8$

To apply the formula for the growth rate you need a meaningful zero point. That means that the values are ratio scaled. If $y_t$ is can be negative as well, then a growth rate cannot be determined.

callculus42
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  • Thanks, but I meant - the revenue itself is negative (the net revenue could be negative even if the gross revenue is positive). So in this example it would be $y_0=100$ and $y_1=-80$ – Alex Craft Jun 04 '20 at 22:51
  • @AlexeyPetrushin I´ve made an edit. – callculus42 Jun 04 '20 at 23:07
  • I see, thanks. I don't know how to find a proper zero point, maybe I'm not forming the question properly. May I ask you to take a look at this slightly different explanation of the issue? https://stats.stackexchange.com/questions/470440/differential-equation-prediction-model-for-future-revenue – Alex Craft Jun 04 '20 at 23:27
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    @AlexeyPetrushin To the iproblem here: Maybe you should compare net revenues only or the gross revenues only. It seems not a good idea to compare net and gross revenues. I´ve to admit that I´m not good in solving recurrence equations. But I´m pretty sure that someone else can help you. – callculus42 Jun 04 '20 at 23:37
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    Thanks anyway :). To be clear - I'm not comparing net to gross. I'm only talking about the net. But it can change the sign, could be that one year it's positive and the next became negative. – Alex Craft Jun 05 '20 at 00:11
  • @AlexeyPetrushin Then it is indeed not meaningful to calculate a growth rate. – callculus42 Jun 05 '20 at 00:15
  • Negative revenue or negative earnings? – Doug M Jun 05 '20 at 00:47
  • @DougM Is the question addressed to me? – callculus42 Jun 05 '20 at 00:50
  • @callculus No, this is really a question for the OP, I suppose. – Doug M Jun 05 '20 at 01:13
  • @DougM negative net revenue (or earnings or net income) - the case when last year net revenue was positive and this year it became negative. – Alex Craft Jun 05 '20 at 04:59