(The) ridge regression for combining forecasts : the multicollinearity case

Abstract

Recent studies have shown that regression approach produces superior combined forecasts when compared to individual forecasts. But because of the collinearity in data matrix, estimated weights are so unstable that the combined forecasts often do not perform better than some of the individual forecasts or a simple average of the forecasts in practice. To solve the problem of collinearity and to provide stable estimates, ridge regression method is applied, which provides a biased estimator yet with smaller MSE than OLS estimator. Prposed is the choice procedure of biasing parameter, k, based on signal-to-noise test by non-central F distribution, which offer the lower bound of k. And we produce upper bound of k guaranting smaller MSE than OLS from the related property of existence theorem. Our bounds are effective in the meaning that they reflect analyst``s prior assumption or conditioning.