How to fill in missing observations in Panel data?

[Santosh]

Hello,
There are some missing observations in panel data.
How to fill in those observations:
1. If the data is missing either at the beginning or end of the series?
2. If the data is missing middle of the series?
3. Suppose the data is missing where the series at that position is clearly increasing or decreasing?

Appreciate your help.
Thank you in advance.

[EViews Gareth]

How do you want to fill them in, mathematically?

[Santosh]

Thank you Gareth for your reply.
Mathematically, it may take time.
I am interested to know how missing obs. are filled in practice, for the three conditions outlined above.
Thank you.