Weighted Quantile Method Of Auto-regressive Time Series

Time series analysis is general statistical method based on data from observations obtained time-sequentially. Many data in our world exist in the form of time series, thus the analytic technique is very popular in statistical works. Compared with other parts in time series analysis the linear time series analysis is most applicable in theory and in practice. This paper will put emphasis on Linear Auto-Regression Time Series Model which is undergoing popular forthputting in statistical practices.The author first introduces general theory of Auto-Regression Model laying foundations for further study, then proposed an improved tactics for its classical statistical methods, in the contrast of classical tools the author prove strong points of new method in estimation of parameters and covariance matrix calculus, and use an example to demonstrate new method’s advantages.The whole dissertation could be epitomized by following clauses:(1) The first chapter introduces auto-regression model and stable solution, then introduces AR model’s spectral density function, covariance matrix and presents theorems on modus to calculate covariance matrix;(2) The second chapter focuses on Weighted Quantile Regression model estimates: definition and some statistical properties, indicating that the main difficulties encountered in the theoretical calculations, lay needs for introducing a solution to the problem in the next chapter;(3) The third chapter is Kern part in the whole paper, is mainly based on the previous proposed weighted quantile regression theory, to smooth weighted quantile regression analysis method and present statistical properties, proposer an iterative algorithm and give steps to calculate covariance matrix and discuss how we choose proper weight function. At last the author talk about parameter hypothesis testing, use data about the amount of rainfall of London from1813to1912to simulate this new method; (4) The fourth chapter is to retrospect the main ideas and methodologies of previous chapters and propose a reasonable idea, about generalizing this new method in vector auto-regression model.The author’s research is to suggest improvements to the classical model of linear time series regression model, making estimation methods derived from the solution more stable and easier to handle in practical calculation, the author hopes the method of this paper can help benefiting research of other linear time-series model.