# Raw interpolation when the desired term is out of the know originals

I was reading this paper regarding the yield curve construction and was programming the Raw Interpolation algorithm (page 7 equation 6) however I was wondering how to use the formula when the desired term is out of the originals. So the interpolation formula is: $$r(t) = \frac{t-t_i}{t_{i+1}-t_i}*\frac{t_{i+1}}{t}*r(t_{i+1})+\frac{t_{i+1}-t}{t_{i+1}-t_i}*\frac{t_i}{t}r(t_i)$$

where $$t$$ is the desired term, $$t_i$$ is the previous known term to the one desired and $$t_{i+1}$$ is the next one. To be clear, my question is how to use this interpolation when $$t or $$t>t_{i+1}$$. At first I thought to set $$t_i$$ or $$t_{i+1}$$ (depending on $$t$$) to 0 but then it doesn't make sense if the original terms goes from 100 to 110 for example.

In other words, you want to "extend" your function $$r$$ for $$t < t_0$$ and $$t > t_n$$.
$$r(t) = r(t_n), \space \forall t > t_n$$
Setting $$t_0 = 0$$ does not require extrapolation for $$t < t_0$$ as time cannot go negative.