Nonlinear Metric Of Multivariate Volatility

Multivariate Time Series Models and Multivariate volatilities Models are traditional methods for Multivariate Time Series Analysis. They all base on one-dimensional Time Series Analysis Models but have some new property. Multivariate volatilities Models could measure the correlation of residual series, they are more compatibility to describe the correlation of Time series than Multivariate Time Series Models, so have a better applicability in Multivariate Time Series Analysis. EGARCH, Fractional integrated Models and some other models are new models of Multivariate Time Series Models and Multivariate volatilities Models, and they provide more applicability to describe Multivariate Time Series.Multivariate Time Series Models and Multivariate volatilities Models also have difficulty in estimation, and poor in describe Heavy-tail and skewness. So copulas have gained popularity in the past few years. A copula function is a multivariate distribution function with standard uniform marginal, by coupling different marginal distributions with different copula functions, copula-based time series models are able to model a wide variety of marginal behaviors. It is also useful to model non-linear correlation of series and capture more correlations of random variables.In order to learn the correlation and dependence structure of volatilities between Real Estate market and stock market, and study the difference of them in short term and long term. This paper modeled National Real Estate Index log-volatility and Shanghai composite index log-volatility respectively by Multivariate Time Series Model, Multivariate volatilities Model and copula-based time series model. Particularly, three indices are used in study of National Real Estate Index. They are the index of selling premises rate, the index of land area development and the index of real estate investment. This paper also learned the correlation and dependence structure of the three indices.