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I am attempting to forecast student enrollment for fall semesters. Enrollment begins about 90 days before the semester starts and closes 20 days after. I have used ARIMA and the forecast package in R to forecast what final enrollment numbers will be for each semester - with pretty decent success. The ARMA model does a good job for the most part, but there are times each semester where enrollment begins to level off, and this leveling off is where the ARMA model has trouble. Up until the leveling off it works great and even after, but what I want to do is forecast enrollment before the leveling off happens.

Is there a way to use ARMA models fitted to data from previous years into my current forecast? Right now I am using forecast() in R with something that looks like this

 X <- enroll_2018
 Y <- enroll_2017
 z <- enroll_2016

 fit_18 <- arima(X, order=c(1,2,2))
 fit_17 <- arima(Y, order=c(1,1,1))
 fit_16 <- arima(Z, order=c(0,1,0))

 enroll <- forecast(fit_18, h=20)

2017 and 2016 are complete and have a model that fits closely to the real data. Is there a way that I can incorporate the arima models from 2016 and 2017 into my forecast for 2018 so I can more accurately forecast when enrollment levels off?

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