The bias-corrected eigenvector approach builds on the idea that if one or more of the predictive models yield biased predictions,
the accuracy of the standard eigenvector approach can be improved by eliminating the bias. The optimization procedure to
obtain combination weights coincides with the standard eigenvector approach, except
that it is applied to the centered MSPE matrix after extracting the bias (by subtracting the column means of the MSPE).The combination weights are calculated as:
$$\mathbf{w}^{EIG2} = \frac{1}{\tilde{d}_l} \tilde{\mathbf{w}}^l$$
where $\tilde{d}_j$ and $\tilde{w}^j$ are defined analogously to $d_j$ and $w^j$
in the standard eigenvector approach, with the only difference that they correspond to the spectral decomposition of the
centered MSPE matrix rather than the uncentered one.
The combined forecast is then obtained by:
$$\hat{y}_t = a + {\mathbf{f}_t}'\mathbf{w}^{EIG2}$$
where $a = E(y_t) - E(f_t)'w$ is the intercept for bias correction. If the actual
series and the forecasts are stationary, the expectations can be approximated by the time series means, i.e. the intercept is obtained
by subtracting the weighted sum of column means of the MSPE matrix from the mean of the actual series. Forecast combination methods
including intercepts therefore usually require stationarity.