Instagram shoutout analytics

Are there any analytics tools to check the best posting time for an account you dont own?

Such as one which analyzes the performance of posts during time certain time periods, and come up with an estimate for which time of day brings the most engagement.

The purpose of this is to analyze the best time to post for an account I do not own, such as for a shoutout.

I really don't know any tools that offers that. But if it is for a shoutout you can ask the page to post the time that it has the most engagement for better results.

Yea I don't think there's a tool for that. Best bet is to ask to see their audience activity from their analytics (of course, if they have a business page).