Smooth Test And Application Of Copula Model

In the field of financial and insurance,most of the time series data has peak and thick tail characteristics.Classical multivariate statistical analysis is not sufficient to describe such time series data,thus introducing a new method for describing the relationship between variables,namely the Copula function.Copula functions are functions that can be used to characterize some kind of correlation between variables.Using the Copula function,we can decompose the joint distribution function into a Copula function and several edge distributions.This property of the Copula function makes the Copula function widely used.A notable feature of the Copula function is its invariance to the rigorous variation of the variables.Fang et al.used the ellipsoid Copula function to construct a class of meta-ellipsoid distributions at arbitrary margins.In the classical multivariate time series model,we generally assume that the new interest segment obeys a multivariate normal distribution.It was later expanded to assume that the new interest segment obeys the ellipsoid distribution.To better describe the multivariate time series,we assume that it obeys the meta-ellipsoid distribution.The meta-ellipsoid distribution consists of an ellipsoid Copula function and a given edge distribution.In multivariate time series analysis,the meta-ellipsoid distribution hypothesis of the vector autoregressive model innovation distribution can describe the multivariate time series data more widely.The normal Copula is usually chosen to construct a meta-multivariate normal distribution.Based on the Cholesky decomposition and the spherical harmonic function,the smooth test of the ellipsoid Copula is proposed.The specific step is to convert the meta-ellipsoid distribution into an ellipsoidal distribution by data conversion,and then convert it into a spherically symmetric distribution,and then convert the spherical symmetric distribution into a spherical uniform distribution,and then convert the hypothesis test of the meta-ellipsoid distribution into a spherical surface.Smooth test method on uniform distribution.In this paper,the maximum likelihood fitting goodness estimation method is used to estimate the unknown parameters of the edge distribution.A simulation estimation algorithm for hypothesis testing p-values is given.The smooth test of meta-ellipsoid is applied to the hypothesis test of the innovation distribution of vector autoregressive model.The metrics of nonlinear correlation between variables based on Copula function are introduced.In the empirical analysis process,the GDP data of the United States,the United Kingdom,and Canada are differentially calculated to obtain the growth rate data of the three countries' GDP.After the estimation of the lag order and the stationarity test of the vector autoregressive model,the vector autoregressive model is established and the impulse response and Granger causal analysis are obtained.The corresponding conclusions are obtained.Under the null hypothesis that the vector autoregressive model innovation distribution obeys the meta-ellipsoid distribution,the goodness of fit of the distribution is tested.Finally,the Kendall rank correlation coefficient and the Spearman rank correlation coefficient between the GDP growth rates of the three countries are calculated.