Research And Application Of Stable Distribution Time Series Based On Laplace Theroy

Alpha stable distribution is often used to analyze non-Gaussian sequences,in particular the distribution of time series and heavy tail characteristics.In this paper,we focus on the theory of Alpha stable distribution.By comparing several common parametric models describing stable distribution,we choose the standard parametric method as the basic data model of this paper.Then,we prove the stability distribution theorem by the Laplace transform to the stable distribution.We get the conclusion that the product of two independent random variables is the random variable with the corresponding distribution,and then make a simulation estimate for the Alpha stable distribution.In the third part of this paper,after introducing the ARCH and GARCH models briefly,we prove the regularity of the GARCH model by Kesten theorem.The regular variation of the joint distribution affects many properties of the derivation process and the correlation between the results,On the basis of the existing theory,the power function of the tail of GARCH model is proved that the finite dimensional distribution of the model is a regular distribution,The Heavy-tailed distribution.Furthermore,it is concluded that the behavior of the tail of the GARCH(1,1)model is more obvious than that of the tail of the residual if the squares of the residuals constitute the corresponding stable random variables.Finally,the residual exponent of the parameters in ARCH(1)is estimated in different intervals.Since the GARCH model can only complete the modeling of a single time series,there are limitations when studying the association of multiple time series.In this paper,we first analyze the necessary conditions for time series modeling,that is,the stationary test of time series,and test the autocorrelation function test and unit root test to test the time series.Then the Copula function is used to study the correlation of multiple time series.GARCH model is used as the edgedistribution of Copula,and the GARCH-Copula model is established for the electric data and building data in the series.And gives the advantages and disadvantages of the fit of t-Copula and normal Copula in finance.It is concluded that the t-Copula model is more suitable for the above data.