# 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 & 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.

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