Predicting when a proportion will reach a certain value Suppose I am trying to model women entering the field of computer science and would like to make a prediction about when the proportion of women in studying computer science in college will reach $.5$.
I have data spanning back several years about the number of women and men entering college for each particular year, and also have a list on the proportion of women in college for some particular year. In other words, 1st list is number of people entering school, and the 2nd list is the total proportion of women across all grade levels. From this yearly data, I would then like to make a prediction about how many years it will take for parity to occur.
What statistical model would work well for this? So far I've only been able to rule out tests that are clearly flawed

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*Linear regression obviously wouldn't be very helpful as we are dealing with proportions and won't want unbounded predictions as time progresses

*Logistic regression seems valid, but having it reach $1$ as time progresses is not desired.

*Beta Regression seemed feasible, but I want to make a forecast rather than a guess on the mean true proportion.

This answer seemed pretty feasible, but a bit hacky and I wanted to know if there was a well established standard way of doing this. It seems like it would be a pretty standard problem (similar with estimating vaccination rates) so I was hoping to gain some insight

As said by Sextus Empiricus it's much more of a "physics" modeling problem than a statistical problem.
I would want a model that takes somwhat a control volume approach:

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*The number of women in CS grows by the number of women graduating CS degrees + some factor of women graduating from other degrees.

*The number of men in CS grows the same way as in 1.

*The number of men/ women decrease by the amount of men/women retiring at the retirement age and some amount of people switching carrers.

*This becomes a differential equation that you need to fit the coefficients to based on the past data you have.

