The purpose of this paper is to compare the upper limits of forecasting error square sum in equal weight forecasting and weighted equal weight forecasting by mathematical induction, and analyze the effectiveness of equal weight forecasting.

This paper aims at obtaining the more accurate value range of optimal combination forecasting error square sum by matrix theory,and presenting some new results of optimal combination forecasting error square sum,and deriving the necessary and sufficient condition when equal weight combination forecasting is optimal combination forecasting with Frobenius theory

In this paper, on the premise that the arid climate system of northwest China is considered, the law of origination and evolution of northwest arid climate is summarized; the prediction theory and method of northwest arid climate, and the relationship between regional climate change and human behavior are qualitatively discussed to some extent.