A Simulation Study To Compare Various Covariance Adjustment Techniques

A common procedure when combining two multivariate unbiased estimates (or forecasts) is the covariance adjustment technique (CAT). Here the optimal combination weights depend on the covariance structure of the estimators. In practical applications, however, this covariance structure is hardly ever known and, thus, has to be estimated. An effect of this drawback may be that the theoretically best method is no longer the best. In a simulation study (using normally distributed data) three different variants of CAT are compared with respect to their accuracy. These variants are different in the portion of the covariance structure that is estimated. We characterize which variant is appropriate in different situations and quantify the gains and losses that occur

A Selective Procedure For Combining Forecasts

If there are various forecasts for the same random variable, it is common practice to combine these forecasts in order to obtain a better forecast. But an important question is how to perform the combination, especially if the system under investigation is subject to structural changes and, consequently, the best combination method is not the same all of the time. This paper presents a data driven approach, which (for each point of time) selects a combination technique from a given set of combination techniques. Properties and limitations of this selection procedure are investigated using simulated data from normal distributions

Linear Plus Quadratic Approach to the Mean Square Error Optimal Combination of Forecasts

This paper deals with linear plus quadratic approaches aiming to find a combined forecast for a scalar random variable from several individual forecasts for that variable. When combining forecasts linear approaches have been used predominantly. One reason may be the well-known fact that the linear approach with constant term is optimal with respect to the mean square prediction error loss, if the single forecasts and the target variable follow a joint normal distribution. In this paper no assumption is made on the type of the joint distribution. Its moments up to order four, however, are assumed to be given for the derivation of the optimal combination parameters. Three versions for the quadratic part of the combined forecast are discussed. As a by-product a linear plus quadratic adjustment of a single forecast is obtained. In order to apply these methods to empirical data the moments of the joint distribution have to be estimated

Regression Approach to the Linear Plus Quadratic Combination of Forecasts

In Troschke and Trenkler (2000) the authors introduce linear plus quadratic approaches to the mean square error optimal combination of forecasts for a scalar random variable. In this paper it is shown how the optimal combination parameters can be obtained with the help of linear regression. Thus numerical considerations as well as application of linear plus quadratic combination to empirical data are facilitated. First results on the comparison of the new methods to the classical linear approaches are given. It is found that there are situations where the linear plus quadratic approaches may be employed beneficially, but further investigations have to be carried out

Some remarks on partial orderings of nonnegative definite matrices

AbstractBaksalary and Pukelsheim (1990) investigated partial orderings of nonnegative definite matrices. Some additional remarks are given in this note