how to do math operations without removing "NA" in time series data in mathematica

Question

I am new to Mathematica and currently working with time series data.

I have the following input data in Mathematica 9.0

data = {{{2011, 3, 13}, 10}, {{2011, 3, 14}, "NA"}, {{2011, 3, 15}, 
    20}, {{2011, 3, 16}, 30}, {{2011, 3, 17}, "NA"}};

Once, I remove the "NA", the data become

data = {{{2011, 3, 13}, 10}, {{2011, 3, 15}, 
    20}, {{2011, 3, 16}, 30}}

I want to do the math operation, such as plus, minus, and mean, without removing "NA" (I want to keep the sequence of date).

For example, in case that I want to divide the values with mean of the data, my output could be

data = {{{2011, 3, 13}, 0.5}, {{2011, 3, 14}, "NA"}, {{2011, 3, 15}, 
    1}, {{2011, 3, 16}, 1.5}, {{2011, 3, 17}, "NA"}};  

Are there any ways that Mathematica can do it? or any suggestions?

Answer 1

data = {{{2011, 3, 13}, 10}, {{2011, 3, 14}, "NA"}, {{2011, 3, 15}, 20}, 
        {{2011, 3, 16}, 30}, {{2011, 3, 17}, "NA"}} /. "NA" -> Undefined;
mean = Mean@Cases[data[[All, 2]], Except[Undefined]];
{#[[1]], #[[2]]/mean} & /@ data
(*
{{{2011, 3, 13}, 1/2}, {{2011, 3, 14}, Undefined}, 
 {{2011, 3, 15},   1}, {{2011, 3, 16}, 3/2}, 
 {{2011, 3, 17}, Undefined}}
*)

Answer 2

You might consider using Indeterminate in place of "NA". When combined with a numeric quantity it evaluates to Indeterminate, e.g.:

1 + Indeterminate
2 * Indeterminate

Indeterminate

Indeterminate

This simplifies tensor operations. Here using DivideBy:

data = {{{2011, 3, 13}, 10}, {{2011, 3, 14}, "NA"}, {{2011, 3, 15}, 20},
        {{2011, 3, 16}, 30}, {{2011, 3, 17}, "NA"}};

data = data /. "NA" -> Indeterminate;

data[[All, 2]] /= Mean @ Select[data[[All, 2]], NumericQ];

data

{{{2011, 3, 13}, 1/2}, {{2011, 3, 14}, Indeterminate},
 {{2011, 3, 15}, 1}, {{2011, 3, 16}, 3/2}, {{2011, 3, 17}, Indeterminate}}