This question is aimed for users who use the REST Tracking API to manually insert visits and actions in Piwik. The parameter cdt lets you define the date and time of the page view. If you set this date to a date in the past (for example, 3 days ago) and that Piwik has already processed the statistics reports for this date, you will not see the newly added data in Piwik.
To tell Piwik that past data was recorded after-the-fact and force the archiving to happen again for this date, you can use the API function: CoreAdminHome.invalidateArchivedReports. For example if you imported data in the past for a few specific websites on a couple different dates you could write:

?module=API&method=CoreAdminHome.invalidateArchivedReports&idSites=1,3,5&dates=2012-01-01,2011-10-15&token_auth=xyz

The next time auto archiving will run will automatically re-process the data for these particular dates.

Note: in rare cases you may want to delete reports for a particular period (one of: day, week, month, year, range). You may set the &period= parameter to the API call, this will force Piwik to only invalidate reports of the specified period.