You can see if you are using iCloud and logout of iCloud by looking at > System Preferences... > iCloud.
You don't need to connect to anything to use Calendars, but your Yahoo! account may be syncing its calendars with the Calendar app. You can check by looking at > System Preferences... > Internet Accounts. Click on your Yahoo! account in the account list on the left, then see if calendars is enabled. If so, you should be able to disable it, then re-enable it, and the calendars should re-sync. You can double-check the Yahoo! calendars to see if that is where your events were, by logging into Yahoo! via a web browser and checking the events there.
If it is not enabled as above, do you have a Time Machine or other backup with which you could recover the local calendars on your Mac from?
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