We use the Pitman-closeness criterion to evaluate the performance of multivariate forecasting methods and we also calculate optimal matrices of weights for the linear combination of multivariate forecasts. These weights are identical with the optimal weights under the matrix-MSE criterion.

An unbiased point estimator T for an unknown parameter θ can be improved in the sense of the Mean Squared Error (MSE) by T = λT λ for suitable factors λ. Here, we want to discuss this approach in the context of combination of forecasts. We consider the shrinkage technique for unbiased...

Error measures for the evaluation of forecasts are usually based on the size of the forecast errors. Common measures are e.g. the Mean Squared Error (MSE), the Mean Absolute Deviation (MAD) or the Mean Absolute Percentage Error (MAPE). Alternative measures for the comparison of forecasts are...

We specify the Pitman-closeness criterion for the evaluation of multivariate forecasts in three categories. This is done closely to the definition of covariance adjustment techniques analysed in other articles. We also apply the Pitman-closeness techniques to an example dealing with German...

Most of the literature on combination of forecasts deals with the assumption of unbiased individual forecasts. Here, we consider the case of biased forecasts and discuss two different combination techniques resulting in an unbiased forecast. On the one hand we correct the individual forecasts,...

In this paper we use 4 different time series models to forecast sales in a goods management system. We use a variety of forecast combining techniques and measure the forecast quality by applying symmetric and asymmetric forecast quality measures. Simple, rank-, and criteria-based combining...