Research On The Volatility Persistence Of Multivariate Time Series

The theory and method of modeling volatility persistence of time series is a powerful tool in analyzing the risk of economic and finance market. Volatility persistence, which have been found in many of time series of economic and finance, indicates that the risk is dependent each other. It raises a new dynamic viewpoint to study the change of risk.. The method of modeling volatility persistence makes a breakthrough for the conventional methods of econometrics in which the risk of economic and finance is considered to be motionless as time changes. The method can accurately estimate the range of volatility risk so that one make it predict and control the future risk to some extant. The method as a effective instrument in analyzing economic and finance risk have attracted more and more attention of economists who come from a variety of research domain. The theory and method in modeling univariate volatility persistence have had full results not only in theory but also in application. There is little knowledge about one of multivariate, however. It is undoubted that the one of multivariate is important to study asset pricing and portfolio and to avoid the risk. Unfortunately, the properties of multivariate volatility persistence are far more complicated than one of univariate. The dissertation is only a tentative beginning of the problem.The dissertation, based on the corresponding research domain of modern econometrics and a variety of references, presents a full summary to the methods of modeling volatility which are very popular in the world. These methods are divided into two types, one is the autoregressive conditional heteroscedasticity (ARCH) models, another is the stochastical volatility (SV) models. The dissertation carefully studies the volatility persistence from the viewpoint of integration and gives a economic explanation for the resource of volatility persistence. Meanwhile, the dissertation detailed analyzes the persistence of the multivariate volatility model and put forward a definition of common persistence from perspective of integration, i.e. if all the components of multivariate volatility model are persistent, but there is some linear combination between components that may have no persistence, and the relationship is defined as co-persistence. The dissertation further considers the properties and conditions of co-persistence and gives the error correction model of co-persistence. The dissertation also presents the ways of estimation and test of co-persistence relationship and compares two type of models by using the ways of stochastic differential equation. At last the dissertation shows that the methodsdiscussed above, when used to analyze capital asset pricing and portfolio investigation, exhibit important effects and implication, and a practice example also gives a satisfied result.The first part of the dissertation (chapter 1, 2, 3) reviews the two type of the methods in modeling volatility persistence which include ARCH models and SV models, and introduces the main results about unit root test of time series and volatility model.The second part of the dissertation (chapter 4, 5, 6, 7) discusses the conception and properties of persistence and put forward a new economic explanation in which volatility persistence is regarded to be corresponding with the hypothesis of fractal market. Meanwhile, the second part gives the definition of the volatility persistence and co-persistence from the perspective of integration and studies the properties and error correction model of co-persistence. In order to estimate and test the co-persistent relationship, the dissertation considers the ways of the single equation and system equation. Chapter 7 of the dissertation compares two type of models from the perspective of stochastic differential equation and persistence and supplies relative proof of mathematics.The third part of the dissertation (chapter 8, 9) applies the results presented above to analyze the risk of finance, and shows the methods to be effective in the aspects of capital asset pricing and portfolio investigation, the dissertation puts forward a simple test method of co-persistence under the condition of the APT. A example of exchange rates is analyzed to indicate the results which are acquired by using the methods presented above to be satisfied.