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Series of Percentage Changes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96789] Series of Percentage Changes
  • From: Gregory Lypny <gregory.lypny at videotron.ca>
  • Date: Wed, 25 Feb 2009 04:01:55 -0500 (EST)

Hello everyone,

We can transform a series to percentage changes by using

	(Differences@theList)/(Most@theList)

or

	(Rest@theList/Most@theList) - 1

However, Mathematica will smartly difference symbols as well as  
numeric values, so the difference of adjacent null elements will be  
zero (Null - Null = 0), resulting in a percentage change of zero, and  
so will adjacent elements with a string, such as "NA" or "Missing",  
that denotes a missing value.  The trouble is, you may want to have  
missing values flagged in the resulting percentage change series just  
as they were in the original series.

I wrote the following little function, which makes use of a Do loop,  
to take care of missing values and instances of division by zero, but  
I was wondering whether there is a more elegant way to incorporate the  
conditions with functions such as Rest and Most and perhaps avoid the  
use of the loop.

percentageChange[theList_] := Module[{tmpList, tmpElements},
    (tmpList = Array[tmpElements, (Length@theList) - 1];
     Do[tmpList[[t - 1]] =
       If[theList[[t - 1]] != 0 && NumberQ[theList[[t - 1]]] &&
         NumberQ[theList[[t]]], theList[[t]]/theList[[t - 1]] - 1,  
"NA"], {t,
       2, Length@theList}];
     tmpList)];


Regards,

Gregory



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