Which is the proper (i.e. grammatically correct) response?
Alice: "The earth is flat, and the sky is green."
Bob: "The earth is round, and the sky is blue."
Alice: "Can you provide indisputable proof of these claims?"
Bob: "No. It's just something I happen to have observed."
Bob: "No. It's just something I happened to have observed."
Best Answer
From the corpus of the Longman Dictionary, it seems the general past tense form is ‘happened to do’. Although I think ‘happen to have observed’ sounds better in your example, as it is not really describing a past case.
(A search led me here because of the title, so I do not think my answer is completely irrelevant.)