The Heteroscedastic Statistical Analysis Based On Compositional Data

In all areas of geology, economic, society, etc, compositional data is a kind of complex data with special structure and is used widely, and each component represents a ratio among each component in the observed object. For example, it can be used to demonstrate the contribution of three industry to the total GDP, predict the trends in industrial structure and study the spending of the residents,etc. Compositional data often appear in the field of finance, management and many other areas, where the phenomenon of heteroscedasticity also happen.As is known to all, one of the main work in financial sector is to discuss the chang-ing market prices, which can be described by variance. Therefore the variance denotes the magnitude of price changes, which is called heteroscedasticity. For instance, the different magnitude of stock price’s changing illustrates that its variance changes with time. It has great significance to describe and characterize this economic phenomenon of financial volatil-ity and analyze the fluctuation characteristics of financial time series for understanding and grasp the development trend and structure of social economic market.This paper first applied the model of heteroscedasticity to the compositional data with particular type. Combining with the property of orthogonal array, we give the parameters estimation in heteroscedastic model and establish the statistical model of different mean-variance about compositional data under the same repeat. This paper is divided into four chapters:Chapter I, Introduction, mainly introduces the research background and status about compositional data and heteroscedasticity.Chapter II, Parameters estimation under heteroscedasticity, mainly puts forward a new method used to estimate the parameters in heteroscedastic model.Chapter III, Different Mean-Variance Analysis Based on Compositional Data, mainly studies a statistical model of different mean-variance about compositional data under the same repeat and its relevant evidence.Chapter IV, Conclusions and Expectation, summarized the main contents of this article and proposes the destination of the future research.