I have at least part of a possible solution.
1. Turn on "Show Missing Values" for your date
2. Use the following calculation that will fill in the empty values with the previous number
IF SUM([Value])>0 THEN SUM([Value]) ELSE PREVIOUS_VALUE(0) END
This gets you about half way there, but I can't think of a way to get the rest of the days (Oct 5 - Today) to show up without adding a dummy row in your data set for today.
Hopefully this can help you get to an answer.