How to extrapolate future probability density functions if you have a time series of them as input?

I'm sorry for lack of technical vocabulary, I'm not a mathematician but an undergraduate student in business informatics.

This is my current situation:

• I am given an observations vector $\textbf{X}$ of continuous variables with a time component $T$ (not equallly distanced).
• My supervisor approximates densities with spatio-temporal kernel density estimation (stKDE) as part of the interpolation.
• I should now extrapolate future pdfs.

My literature research has resulted in some areas I think could be of use to solve my problem:

• Methods of functional data analysis (FDA) combined with time series analysis?
• Methods of symbolic data analysis? (SDA)
• Conditional kernel density estimation? (cKDE)

I only need some hints that will point me into the right direction and I would be glad if somebody can help me out.

• Perhaps you could add some context on what problem you're trying to solve with this modeling? Several questions come to mind. Is there a "space" variable as well, since your supervisor is using stKDE? Are you trying to test that the pdf doesn't change over time ("stationary" concept from time series analysis)? Are you trying to control a process (then various quality control methods are useful)? Are the data autocorrelated (again, a time series concept)? Again, some context on why you're doing this will help determine appropriate methods. – blackeneth May 17 '15 at 8:14