| 论文摘要 | 第1-7页 |
| ABSTRACT | 第7-8页 |
| Résumé | 第8-13页 |
| List of Tables | 第13-15页 |
| List of Figures | 第15-20页 |
| 1 Introduction | 第20-27页 |
| 2 Some Probabilistic Properties of Stationary Processes | 第27-47页 |
| ·Introduction of Stationary Processes | 第27-30页 |
| ·Short Memory Processes | 第28页 |
| ·Long Memory Processes | 第28-30页 |
| ·Self-similar Properties for Stationary Processes | 第30-47页 |
| ·Concepts of Self-similarity | 第30-32页 |
| ·Continuous-time Self-similar Processes | 第32-34页 |
| ·Discrete-time Self-similar Processes | 第34-36页 |
| ·Examples of Self-similar Processes in Continuous Time | 第36-39页 |
| ·Examples of Self-similar Processes in Discrete Time | 第39-45页 |
| ·Summarize for the Self-similar Processes | 第45-47页 |
| 3 Wavelet Techniques for Time Series Analysis | 第47-61页 |
| ·Introduction of the Time-frequency Representations | 第47-49页 |
| ·Fourier Transform | 第47-48页 |
| ·Short-Time Fourier Transform | 第48页 |
| ·Wavelet Transform | 第48-49页 |
| ·Properties of the Wavelet Transform | 第49-51页 |
| ·Continuous Wavelet Functions | 第49-50页 |
| ·Continuous versus Discrete Wavelet Transform | 第50-51页 |
| ·Discrete Wavelet Filters | 第51-53页 |
| ·Haar Wavelets | 第52-53页 |
| ·Daubechies Wavelets | 第53页 |
| ·Minimum Bandwidth Discrete-time Wavelets | 第53页 |
| ·Discrete Wavelet Transform (DWT) | 第53-56页 |
| ·Implementation of the DWT:Pyramid Algorithm | 第54-56页 |
| ·Multiresolution Analysis | 第56页 |
| ·Maximal Overlap Discrete Wavelet Transform (MODWT) | 第56-58页 |
| ·Definition and Implementation of MODWT | 第57页 |
| ·Multiresolution Analysis | 第57-58页 |
| ·Discrete Wavelet Packet Transform (DWPT) | 第58-60页 |
| ·Maximal Overlap Discrete Wavelet Packet Transform (MODWPT) | 第60-61页 |
| 4 Estimation Methods for Stationary Long Memory Processes:A Review | 第61-88页 |
| ·ARFIMA Processes | 第63-77页 |
| ·Parametric Estimators | 第65-67页 |
| ·Semiparametric Estimators | 第67-70页 |
| ·Wavelet Estimators | 第70-77页 |
| ·Seasonal and/or Cyclical Long Memory (SCLM) Models | 第77-87页 |
| ·Estimation for the k-factor Gegenbauer ARMA Processes | 第79-86页 |
| ·Estimation for the Models with Fixed Seasonal Periodicity | 第86-87页 |
| ·Seasonal and/or Cyclical Asymmetric Long Memory (SCALM) Models | 第87-88页 |
| 5 Estimation and Forecast for Non-stationary Long Memory Processes | 第88-115页 |
| ·Fractional Integrated Processes with a Constant Long Memory Parameter | 第90-91页 |
| ·Locally Stationary ARFIMA Processes | 第91-93页 |
| ·Locally Stationary k-factor Gegenbauer Processes | 第93-101页 |
| ·Procedure for Estimating d_i(t) | 第95页 |
| ·Estimation Procedure | 第95-97页 |
| ·Procedure for Estimating d_i(t)(i=1,…,k) | 第97-99页 |
| ·Consistency for estimates d_i(t)(i=1,…,k) | 第99-101页 |
| ·Simulation Experiments | 第101-105页 |
| ·Forecast for Non-stationary Processes | 第105-115页 |
| 6 Applications | 第115-168页 |
| ·Nikkei Stock Average 225 Index Data | 第115-135页 |
| ·Data Set | 第115页 |
| ·Modeling | 第115-121页 |
| ·Forecast | 第121-135页 |
| ·WTI Oil Data | 第135-167页 |
| ·Fitting by Stationary Model:AR(1)+FI(d) Model | 第136页 |
| ·Fitting by Stationary Model:AR(2)+FI(d) Model | 第136-147页 |
| ·Fitting by Non-stationary Model Using Wavelet Method | 第147页 |
| ·Forecast | 第147-167页 |
| ·Conclusion | 第167-168页 |
| 7 Testing the Fractional Order of Long Memory Processes | 第168-181页 |
| ·Unit Root Test for Autoregressive Moving Average Processes | 第169-170页 |
| ·Unit Root Test for Fractional Integrated Processes | 第170-181页 |
| 8 Conclusion | 第181-185页 |
| ·Overview of the Contribution | 第181-183页 |
| ·Possible Directions for Future Research | 第183-185页 |
| A The Well-definedness of the Locally Stationary k-factor Gegenbauer Pro-cesses | 第185-187页 |
| Bibliography | 第187-203页 |
