Research And Analysis Of Time Series Model Based On Stable Distribution

It's very important to analyze and process data under the conditions of massive data. Time series analysis is a method of dynamic analysis and processing which is widely used.Our paper firstly describes the definitions of the alpha stable distribution, properties and features of probability and statistics as a basis for theoretical research. Through simulation method to clarify the meaning of all parameters of the alpha stable distribution. And then use the stable distribution parameters in common to re-label alpha.Finally concluded that applies to the nature of the standard parameter is also applicable to other parameters, and gives its transformation relationship, and explores the under different parameters of the probability density function of the direct integral method.Then we discuss several ways to test the stability of time series, mainly auto-correlation function and unit root test method. We comparative analysis several test methods of the application and performance advantages and disadvantages by way of example. Autocorrelation function method is intuitive and convenient, but the result is roughness. DF test method is applicable to random disturbance irrelevant AR(1) model. ADF test is suitable for the model that innovations is homogeneous of variance.Finally, this paper show the asymptotic distribution of M-estimators in no stationary AR(p) processes where error on the domain of attraction of a stable law with index a?]2,0(.We analyze time series model and linear residual error model by using the least square method and correlation analysis.This paper finally solve the following problems: clears the relations of the random variables between the different parameter systems, obtains the properties based on the standard parameterization under the other parameterizations expression form, calculates method of probability density function; Throughcomparing examples of autocorrelation function method?DF test and ADF test with the applicable condition and performance on the data stability test; Presents the asymptotic distribution of M-estimators in no stationary AR(p) processes with infinite variance and autoregressive analysis for time series model.This paper finally solve the following problems:clears the relations of the random variables between the different parameter systems, obtains expression form of the properties based on the standard parameterization under the other parameterizations, calculates method of probability density function;Through comparing examples of autocorrelation function method?DF test and ADF test with the applicable condition and performance on the data stability test; Presents the asympotic distribution of M-estimators in nonstationary AR(p) processes with infinite variance and autoregressive analysis for time series model.