Mathematical Modeling Of Change-point In Economics, Finance And Econometrics & The Research And Application Of The Change Of Structure

This recent year, the problem about change point is always one of the hot issues in the leading field of the research of statistics. There is profound signification in theory and there is important value of the application. At the same time, it is already applied to various subjects. Such as economics, finance, iatrology, physics, geography, literature. Especially, in the economic and financial fields the application of change point is sufficiently abroad.We have got research fruit full of value about Change Point not only in theory but also in application in the past few years. But there is something worthy of our further research. It requires dealing with more and more the economic and financial problems in the modern society of developing at very fast speed in economy. In this paper, we apply the change point to the linear regression about the consumption and income of resident in our country, and examine the linear relation between the consumption and income whether they are changed. And we gave a simple and quick method that we combined validly the binary segmentation with Schwarz Information Criterion to find the amounts and the positions of the change points correctly. It can overcome the defect of checking up only one change point in the traditional method. When dealing with economic model, it exists universally two problems that are the autocorrelations of residual error and the correlations between residual errors by Koyck transformation in Geometric Distributed Lag Model. In allusion to the simultaneity of the two problems, we give a particular estimation method that we combine the method of Instrument List with the method of Generalized Difference. Then we can make mathematical model exactly, and explain economic question, take the corresponding economic measures.With the enlarging of the scale of the financial trade in the securities business increasingly, the risk of price is also increasing. The risk of the money market is incapably avoidable, the stock index futures is just the tool of the elusion system risk availably. Stock index futures have three functions of hedging arbitrage and speculate as a derivation financial tool. Thereinto, hedging is the most basic investments strategy. In this paper, in allusion to hedging, which is used to avoid market risk. We give another inimitable method to analyze. Different obviously, it is estimated by price difference between the market of merchandise on hand and futures. Then it is traded in two different markets, in order to payoff steadily in the two markets to avoid the risk. But the traditional method is that we payoff by merchandising futures agreements in futures markets to offset the loss in the market of merchandise on hand. Besides, we go to discuss the question about the contract that is moral hazard with private information under the circumstance of asymmetric information between the principal and the agent, and the method of discussing the question is deserved commending and generalizing. It has practical value commendably and research signification to the designing of the best incentive contract.