Long-term Memory Parameter Estimation Based On Bootstrap

This thesis mainly compares and analyzes the applicability of the method under long memory time series by Block Bootstrap.Firstly,the development of the model ARFIMA,a popular long memory model,is reviewed and introduced,and then the long memory parameters estimation method-GPH estimator,R/S estimator and variance plot estimator are introduced.The theoretical basis,generation process and asymptotic properties of the estimation method are briefly described.Based on the simulated long memory data,the ARFIMA(0,d,0)model is used for adaptive testing.It was found that the lengths of different sampling blocks under the bootstrap test slightly affect the results.In general,the effect of the confidence interval is significant when the sample size is small.This is in line with the initial intention of the bootstrap method for small samples.However,analysis and comparison of the three estimation methods under the bootstrap parameter d estimates show that the R/S method and Variance Plot method are more accurate,while GPH estimates is often lower.The selection of the estimation method is particularly important when we use bootstrap to estimate long memory degree.On the empirical side,the study mainly focused on the domestic and foreign gold market price rate of return and volititlity.Through the long memory recognition method,it was verified that domestic gold AU9999 and London gold have significant long memory,and through comparison,the long memory of international London gold was discovered at slightly higher level.The bootstrap also effectively controls the 95%confidence interval in the experiment.