Missing Data

If predicting $\nu(t)$ we don't know some value of then We replace the missing data $\nu(s),\ s<t$ by the expected value $\hat{\nu(s)}$ defined as

$$\hat{\nu(s)}=\sum_i^p (a_{1i} \nu(s-i)+a_{2i} \eta(s-i)),\ p < t < T_0$$ (25)

The least squares estimates of the regression parameters $a_{1i},\ a_{2i}$ are obtained using observations previous to the missing one by minimizing expression (1.22) . The same idea can be is extended, if two or more values of the factor $\nu$ are missing.

This algorithm is used to "fill" the missing data only for the predicted factor $\nu$. We replace missing values of the external factor $\eta$ by the nearest previous value, because we do not predict the external factors in this model.