How to extrapolate the data? I have bond yields for Indian G-Sec. For short term yields the proxy are (15-91 days) , (92-182 days) , (183-364 days). For long term yields the proxy are 5,10 &amp; 15 years. Data ranges from 1996 - 2016.
But the yield values for 15 years bonds are unavailable from 1996 to 1999. So in order to have a complete data-set, i need to compute the 15 year bonds yield those 3 years on monthly basis.

Please check the below link for data file.
https://spaces.hightail.com/space/9wrYy
You are never going to be able to fill in the gaps exactly, so the best approach may depend on what you want to use the data for.  

One reasonable approach might be to use an average offset from the 10-year rate, e.g. adding about $0.3$ to it.  If you did that, then you would get the red data on the chart below, which compares reasonably well with the actual blue data for the 15-year rate, though not perfectly.  So you might use the red line as a proxy for the earlier missing blue data.  This might not be such a good idea if the purpose of your analysis was precisely considering the changing gap between the 10-year and 15-year rates