Long Memory Time Series And Empirical Analysis

The traditional time series theory has become mature, it base on the short memory characteristic. But lots of time series have performed long memory characteristic in our life. From this point of view, this paper has researched and analyzed the long memory time series in detail.At first, this paper has introduced the research status in quo and its application background. In Chapter 2, it also introduced the tradition time series model, and from the disadvantage point that traditional time series model can not simulate the long memory time series well, so long memory time series theory is proposed.In Chapter 3, firstly, this paper has defined long memory concept. Then it analyzes how to verify the long memory characteristic in a time series. Lastly, the paper presents the fractional differenced noise model and the autoregressive fractional integrated moving average model.In Chapter 4, this paper define self-similar concept. From the definition of self-similar we can easily know that self-similar series perform long memory characteristic. It is a particular performance of the long memory time series. The paper has used a network traffic which comes from CERNET to make a demonstration. Through investigate in the network traffic by R /S analytical method, I found that the network traffic has self-similar and long memory characteristic. It also performs short memory characteristic through change the time series original scale. Lastly, the paper indicates that in order to analyze the feather of self-similar and long memory in the time series exactly, it needs enough data to support. And it will refuse the hypothesis that the long memory time series have long memory characteristic while there isn't enough data to support.