Matrix Analysis In The Prediction Theory

This paper mainly includes two parts:In part one (chapter 2), we obtain the general expression of errors square sum J c in VWCF (variable weight combined forecasting method) problems, then the optimizing model of VWCF is presented:Furthermore, based on the idea of variance reciprocal weight method, the error reciprocal variable weight combined forecasting method (ERVW) is developed. In ERVW, the weighted coefficient of the i th forecasting method in the t th forecasting subperiod can be assumed as follows: where And the errors square sum of ERVW is whereFinally, the example shows that ERVW method is feasible, and it's better than optimal combined forecasting method.In part two (chapter 3), we improve on a sufficient condition when the optimal weighted coefficient is non-negative which is presented in reference [28]. Under the same hypothesis, a more accurate conclusion, by applying the M-matrix theory, is derived:When the information matrix of forecast errors E _n satisfies E _n∈Z^{n ,n}, the optimal weighted coefficients are all positive.Furthermore, a very simple proof of the sufficient condition in reference [28], by...