The Mathematical Study Of The Financial Crisis Forewarning Of Manufacturing Industry Listed Company

With the intensifying of economic globalization and the further deepening of Chinese socialist market economy, enterprises are facing fierce competition and tough challenges at all times. In the competitive market environment, some enterprises will inevitably fall into the financial crisis, and even the emergence of the crisis of survival. Financial crisis is a systemic problem of effects of market stability. Therefore, the research on enterprise financial crisis has attracted more and more attention in recent years.In this paper, the Shanghai and Shengzhen A shares of listing Corporation in manufacturing industry is used as the research object, we choose 18 ST listed listing Corporation in 2008-2009 years and their pair 18 non ST listing Corporation as modeling samples, and select the 13 ST listing Corporation in 2010 year and its paired 13 non ST listing Corporation as testing samples. According to the standard of selecting the study of financial crisis early warning index at home and abroad, we select 17 financial ratios as the original financial index system, and we conduct the index difference test of financial indicators of the modeling sample to screen out the financial indicators which have significant differences, the financial indicators will be used to build the prediction model. The financial index data of the modeling sample in t-1 and t-2 years are used to construct the early warning model of financial crisis based on principal component analysis, then we use the corresponding financial index data of the test sample to detect the prediction model, the accurate rate in t-1 and t-2 years were 96.15%, 88.45% respectively, it indicates that the warning model which is constructed based on principal component analysis method has good prediction ability. The principal components which is obtained by principal component analysis method is hard to explain, thus it is lack of practical guiding significance. Therefore, we need to make corresponding improvement on model method. We present a sparse principal component analysis method to make the improvement of the principal component analysis method in order to improve the interpretation model. Finally, we establish respectively the early-warning model based on our sparse principal component analysis method, and their model accurately rate is 92.31%, 84.6% respectively.. According to the result of accuracy of the model prediction, the closer distance to financial crisis time is,the higher the prediction accuracy of financial crisis early warning model is. In contrast, the prediction accuracy of the model is lower.Empirical results show that sparse principal component analysis method is s uitable for the early warning of financial crisis.Not only are consistent the predi ction effect of the method and the principal components results, but also we can more clearly analyze financial factors which impacts the financial situation of e nterprises after sparsing the load of principal components.It can make the guida nce better to carry on the early warning of enterprise financial crisis, and takin g corresponding measures to avoid risk, thus it has the very good practical signif icance.