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 for February I have 20  revenue    My growth would be   20-10  10  100    100      If I have 0  revenue for March    Then my growth would be   0-10  10  100    -100    Should I call this as negative percentage   I know its deflation   Going one step further       If now I have  20  revenue  for April    How can I calculate the growth now   sure the following formula is wrong    20-0  0  100           My basic questions are   Is there a better solution to find growth rate  other than the one above  If I use the aforementioned formula  should I take some value as reference  or this is wrong also

User · Answer

When both values are zero  then the change is zero  If one of the values is zero  it s infinite  ambiguous   but I would set it to 100   Here is a C   code  where v1 is the previous value  old   and v2 is new   double result   0  if  v1    0  amp  amp  v2    0         If values are non-zero  use the standard formula    result    v2   v1  - 1    else if  v1    0    v2    0         Change is zero when both values are zeros  otherwise it s 100     result   v1    0  amp  amp  v2    0   0   1    result   v2  gt  v1   abs result    -abs result      Note  To have format in hundreds  multiply the result by 100

User · Answer

It should be  new minus old  mod avg of old and new With a special case when both val are zeros

User · Answer

use below code  as this is 100  growth rate in case of 0 to any number    IFERROR  NEW-OLD  OLD 100

User · Answer

There is no rate of growth from 0 to any other number  That is to say  there is no percentage of increase from zero to greater than zero and there is no percentage of decrease from zero to less than zero  a negative number   What you have to decide is what to put as an output when this situation happens  Here are two possibilities I am comfortable with    Any time you have to show a rate of increase from zero  output the infinity symbol  8   That s Alt   236 on your number pad  in case you re wondering  You could also use negative infinity  -8  for a negative growth rate from zero  Output a statement such as   Increase Decrease  From Zero  or something along those lines    Unfortunately  if you need the growth rate for further calculations  the above options will not work  but  on the other hand  any number would give your following calculations incorrect data any way so the point is moot  You d need to update your following calculations to account for this eventuality   As an aside  the   New-Old  Old  function will not work when your new and old values are both zero  You should create an initial check to see if both values are zero and  if they are  output zero percent as the growth rate

User · Answer

This is most definitely a programming problem  The problem is that it cannot be programmed  per se  When P is actually zero then the concept of percentage change has no meaning  Zero to anything cannot be expressed as a rate as it is outside the definition boundary of rate  Going from  not being  into  being  is not a change  of being  it is instead creation of being

User · Answer

There are a couple of things to consider    If your growth is 0 for that month  it d be 0 in change from 0  So it is meaningful in that sense  You could adjust by adding a small number  so it d be change from 0 1 to 0 1  Then change and percentage change would be 0 and 0     Then to think about case where you change from 0 to 20  Such practice would result in massive reporting issues  Depending on what small number you choose to add  eg if you use 0 1 or 0 001  your percentage change would be 100 fold difference  So there is a problem with such practice    It is possible however if you have a change from 1 to 20  then the  change would be 19 1 1900   Here the   change doesn t make too much sense when you start off so low  it becomes very sensitive to any change and may skew your results if other data points are on different scale   So it is important to understand your data  and in this case  how frequent you encounter 0s and extreme numbers in your data

User · Answer

If you re required to show growth as a percentage it s customary to display  NaN  or something similar in these cases  A growth rate  on the other hand  would be reported in this case as   month  So in your example for April the growth rate would be calculated as   20-0  1   In any event  determining the correct method for reporting this special case is a user decision  Is it covered in your user requirements

User · Answer

You can add 1 to each example New   5  old   0   1 new  -  old 1     old  1  5  1   100    gt  500

User · Answer

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

[math] How to calculate percentage when old value is ZERO

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