The Problem Of Martingale Transform Parameters Estimate For Auto Regression Moving Average Model

To a certain extent, consumer confidence index is a reflection of the status of economic development. This paper researches the parameters of the model estimation problem based on this index established by stationary time series model. Thesis as follows:Firstly, paper introduces a new estimate of the parameters of stationary time series model estimation method and gives the proof of two. On the one hand, integral function is a function to be integral to the martingale transformate the orthogonal projection of space. On the other hand, when the kernel function selected from a countable concentration, the transform function can approximate integral function integral. These prooves to optimize the martingale transform estimation function provides a theoretical basis. Then paper proposes a conjecture for the martingale transform estimate function optimization problems.Secondly, paper analyzes the consumer confidence index of the timing diagram. Through the stationary time series model identification methods, paper choices AR model. Then through SAS software, paper calculates the data autocorrelation and partil correlation coefficient and selectes the order of the appropriate stationary time series model fitting and optimization.Thirdly, by using the real-valued kernel function, paper constructs a martingale transform to be integral function and by using MATLAB, paper analyzes the asymptotic approximation on the sructured function. It obtains the quasi-maximum likelihood parameter estimation. For the consumer satisfaction index model and the consumer expectations index model, paper obtains the quasi-maximun likelihood parameter estimation through the analysis of approximtion to be different martingale transformation integral function.Finally, through the SAS software, three different models are predicted and then paper validates the method which used to estimate the effectiveness of AR model parameters.