ESR Interest Rate Forecast

$$\begin{array}{lll}{f}_{i,t}& =& \overline{f}\exp (\frac{Y_{i,t}}{\overline{f}}-1)\{Y_{i,t}<\overline{f}\}+f_{i,t}\{Y_{i,t}>\overline{f}\}\\ R(t,{\tau }_i)& =& \{\begin{array}{c}{f}_{i,t}\text{if}i=1\hfill \\ (1-\frac{{\tau }_{i-1}}{{\tau }_i})f_{i,t}+\frac{{\tau }_{i-1}}{{\tau }_i}R(t,{\tau }_{i-1}),\forall i⩾2\end{array}\end{array}$$