Empirical Research Of Treasuries Indexes Using ARMA-GARCH Models

Since the European debt crisis occurs, many economists andmeasurement statisticians begin to focus their attentions on the Treasury bondmarket. The national debt, which is the reflection of national credit, has thevalue of revealing the national credibility. Therefore, it will be a verymeaningful issue to make quantitative data analysis and prediction of theTreasury bond market trend with the measurement statistics tools to achievethe purpose of risk control.In this thesis, we mainly use the ARCH type models to study ourcountry’s Treasury index yield sequence. Through the research, we find that, itwill present a certain serial correlation because of its own data joint inertiaand backwardness relative to economic and policy. Therefore，ARMA model isused to describe the Treasury yield sequence, and GARCH model is used to fiterror. Meanwhile, considering both the financial data’s peak thick tail andheteroscedasticity, and the bias of the ability which investors bear in the riskinvestment, we establish the ARMA-GARCH model with the error distributionbased on Normal, GED and Student’s t distribution respectively, because itmeets the fact more and has better research effects. Moreover, we attempt touse the method of cross validation to predict the trend, and get better results.The details are given as follows:The first chapter elaborate the research background of this thesis and theresearch situation of the home and abroad briefly, besides, put forward theresearch purpose and analytical methods of this thesis.The second chapter is a brief overview of the structure of ARCH typemodels related in the article, which mainly contain the introduction ofARMA-GARCH models with different error distributions.The third chapter get some basic statistical analysis of fat tail, bias,self-correlation, stationarity and Heteroscedasticity with Eviews5.1,viaanalyzing the characteristics of treasuries indexes returns’ series, to determinethe appropriate analytical model.Chapter four estimate the parameters of ARMA(p,q)-GARCH(r,s)models, by AIC criterion, to determine the appropriate ARCH type models to fitTreasury index yield sequence, and predict treasuries indexes trend With theCross-validation. Compare the different models with the different errordistribution in the aspects of fitting and predicting result respectively, to findmore suitable models for the research of treasuries indexes.Chapter five:Conclusion.