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I have as target variable probability (observed/realised p over time) so its p~(0,1). I'm looking for the right model to fit the observed probability over time and "predict" n steps ahead.

I'm not sure, I tried to fit just normal glm (family=quasibinomial) but how to insert the dynamics (component time)? I'm not sure whether to resort to time-series model in this case since I have discrete finite observations ~(0,1) however I have time "time-component" so the dynamics over time matters, I guess.

glm(probability~time, data, family=quasibinomial, weight=1:nrow(data))

possible sample data:

data <- data.frame(probability=runif(100), time=1:100)

Could survival model be appropriate here? Thank you for any hint.

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