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By regressing $r_{i,t}$ on $y_{i,t}$ you are implying that: $$ r_{i,t} \equiv y_{i,t} - y_{i,t-1} = c_1 y_{i,t} + c_2 + \epsilon_{i,t}$$ This seems quite odd to me initially. If you assume that daily yield changes are independent with mean zero, then; $$ y_{i,t} = y_{i,t-1} + \xi_{i,t} \; \quad E[\xi_{i,t}]=0$$ Which can be replicated in the linear ...

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