Abstract
Stock price index has always been playing the role of barometer of national economy. In recent years, with the rapid development of securities market, the scale of investment is getting larger. However, the innovation process of index products is still restricted because of comparable slow development of stock price index and inventors’ inadequate knowledge about index. Therefore, quantitative analysis upon stock price index is very vital and indispensible. Many institutions take component-shares as one of the four indices which are financial index, estate index, commercial index and public index. This paper aims to figure out the general situations of stock price index during different periods by analyzing both main components and factors of the four indices. Then shows the balance relations among stock price indices by using Co-integration analytical method.
Main-component analysis is a statistic method that changes several indices into fewer indices. In this paper, main-component analysis of the four indices will firstly be given. From the main-component analysis results of SPSS, we can see there are two eigenvalue whose accumulate contribution rates are at 95.485%, which means former two main components have already indicate all information that the four indices want to show. And expressions of the two components can be worked out after knowing their eigenvectors which may be gained through original gene-load matrix.
When analyze the factors of the four indices, we will obtain two common factors which owns economical effects by the means of variance maximum orthogonal rotation. One is a profitable factor that basically dominates financial index, estate index and commercial index, three of the four indices. The other is a common factor that basically controls the public index. According to the main-component scoring coefficient matrix, we can get the factor scoring model of stock price index so as to show evaluating score of separate main component. After the analysis towards factors, taking the proportion of factor scoring and separate variance contribution rate as standard to evaluate generally, we can finally figure out a general scoring expression of stock price index during every period.
During the process of research the relation between time sequences, making regresses between apparent unstable sequences will be ended up wrong conclusion, which might be “false regress”. This paper adopts Co-integration analytical method to assure the connections between unstable sequences. First of all, make an inspection towards unit roots of the four stock price indices in order to prove that they are all Integration Process sequences. Then make full use of least-two multiplication to Co-integration inspection. For those inspected residual sequences boast stability, the four stock price indices are Co-integrated. That is to say that there are long-term balanced relations among them.
