Some additional observations or reminders:
When applying for a PR card or for citizenship, it is the PR's obligation to report all travel dates. The burden is squarely on the PR. Thus, Canadian PRs should keep precise records documenting dates of travel abroad (including to the U.S.), and records regarding place of residence, employment, and other aspects of living in Canada.
U.S. citizens living abroad should keep precise records of travel dates to the U.S. While the importance of this is dependent on the individual's tax filing status, typically the U.S. citizen should have this information to report (in tax returns) if necessary.
Reminder: for U.S. citizens living abroad, the threshold for mandatory filing of U.S. tax return is minimal, even for a U.S. citizen who does not visit the U.S. at all. The threshold for FATCA filing requirements (pursuant to which all U.S. citizens are required to report details about bank and investment accounts outside the U.S.) is a mere ten thousand dollars total, that is the total of all accounts combined, including amounts in joint accounts or accounts for which the U.S. citizen has any interest in or signatory authority for. Penalties for failure to make this annual filing are severe: there is a ten thousand dollar penalty even if there are NO taxes due, even if the failure to report has no significance other than the mere failure to report. Best case scenario can still be incredibly expensive.
Reporting estimated past travel dates:
Again, when reporting travel history for either a PR card application or for a citizenship application, it is the PR's obligation to accurately and completely report ALL dates of exit from Canada and dates of entry into Canada.
PRs who failed to keep a record of their travel need to reconstruct, as best they possibly can (and this means putting some serious effort into it), their travel history. The PR should readily acknowledge and explain, on a separate page, any uncertainty about the reported travel, and provide a detailed estimation of any travel not specifically reported.
thecoolguysam identified some resources for obtaining what information the respective Canadian and U.S. authorities might have regarding travel dates. These can be used to assist the PR's effort to fully reconstruct travel dates, but should not be relied upon to be complete. Additional sources of potentially helpful information includes credit card history, email references to trips, recollection of family and friends, history of time off work or out of school related to travel, and so on.
For a PR card application, the PR who has been long settled in Canada, living in Canada, and for whom the total amount of absences compared to time spent in Canada is relatively small, some estimation as to the number of trips and time abroad should not cause a problem. If in addition the PR has been working in Canada, or living with a Canadian citizen spouse, the risk of a problem is even lower. Far better to report all travel accurately, but for the PR who is well settled in Canada the risks are low for at least the first PR card renewal.
Thus, for the PR card, while the PR should make a concerted effort to accurately reconstruct the travel history, the PR who is settled and living in Canada probably has no reason to worry if the PR makes a reasonable effort to report his or her travel history.
When applying for citizenship, however, the applicant needs to get really close to accurately reporting all travel. Then the PR needs to make a dedicated effort to reconstruct precise dates and to at least report an accurate number for all overnight trips.
Again, while the information the U.S. and Canada can provide will be helpful, it cannot be relied upon to be complete.
