Each member of the hierarchy has the "HideMemberIf" property. Setting this parameter to "NoName" should hide the null values in the size browser and allow cube processing.
You can also create named calculations in the Datamart view. The named calculation will use the ISNULL function, which can populate values instead of zeros. Then, of course, build a time dimension from these Named calculations instead of raw data fields.
Again, it's best not to have any zeros in your data at all, but usually you can fix this inside the cube.
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