Scalar Prediction

In this section we apply the ARMA model to describe and to predict the errors $\nu_i$ of the expert model $\psi_i(s,d,\tau)$ defined in the previous section where $\nu_i=\psi_i(s,d,\tau) -z_i$ The theoretical considerations are in [] . The formal description of the ARMA model is in chapter 1. The software is on web-sites (see section ).

If predicting $\nu_i$ we don't know some values of $\nu_s,\ s=i-1,i-2,...$ then we replace the missing data by the expected values of the unknown $\nu_s$ defined recurrently (see section 2.12).

Note, that here ARMA models predict only the difference between the expert models (EM) and the data. In the first step, EM models are adapted to the data by defining the right scales. Only then, the parameters $a,b$ of ARMA models are optimized by minimization of a squared difference between the adapted EM model and the observed data. Predicting the data, the results of both EM and AH models are summed up.