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Currently I scheduled a task to extract twitter data of a week (every sunday) to predict the stock market for the following days. The number of likes of a tweet is not static and changes over time. Tweets posted and extracted on weekends are less likely to reach their "true" number of likes and other characteristics.

Calculating an expected value for the number of likes based on early periods after a tweet got published seems unreasonable as this would heavily depend on the user and other factors I can't control.

What a ways to work with this kind of data so that a tweet that really got almost no likes on Monday (had 5 days time to get likes) and a tweet that is going to go wild do not look the same for my algorithm?

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So basically your problem is that you don't know what the future will bring, in your case how the number of likes for a tweet will develop after you collected the data. Welcome to the club... All we can do when it comes to predicting is to give our best guess and be ready to be wrong. It is logically impossible to get an empirical foundation for a prediction other than waiting till the time has passed, at which point the prediction lost its value... You can of course extrapolate from past experience, and this can often be helpful, but not perfect. Extrapolation is especially horrible at predicting new developments, for obvious reasons.

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