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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 $2 \times 1.06^2 = 2.25$

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  • $\begingroup$ Why not the same formulas? You'll have ratios smaller than one (because $y_{i+1}<y_i$), and that should be fine. $\endgroup$
    – user239203
    Commented Jun 4, 2020 at 22:07
  • $\begingroup$ Revenue is negative, earnings are negative, or revenue growth is negative? $\endgroup$
    – Doug M
    Commented Jun 5, 2020 at 1:14
  • $\begingroup$ @DougM the revenue became negative 2001 revenue = $1M, 2002 revenue = $-1M $\endgroup$
    – Alex Craft
    Commented Jun 5, 2020 at 4:07

1 Answer 1

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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.

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  • $\begingroup$ 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 $y_1=-80$ $\endgroup$
    – Alex Craft
    Commented Jun 4, 2020 at 22:51
  • $\begingroup$ @AlexeyPetrushin I´ve made an edit. $\endgroup$ Commented Jun 4, 2020 at 23:07
  • $\begingroup$ 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? stats.stackexchange.com/questions/470440/… $\endgroup$
    – Alex Craft
    Commented Jun 4, 2020 at 23:27
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    $\begingroup$ @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. $\endgroup$ Commented Jun 4, 2020 at 23:37
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    $\begingroup$ 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. $\endgroup$
    – Alex Craft
    Commented Jun 5, 2020 at 0:11

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