Need to edit my suggestion - as I only realized now, that you don't have any previous values for Y at all (note to self: reading skills are a plus).
In this case my suggestions below won't work of course.
Hello -
Time series models typically deal with missing values well, if there are only few. So you might want to try your data as is first.
As another idea, you may want to use an exponential smoothing model for your Y series first, and use its predictions to impute missing values of Y.
Thanks,
Udo