Chapter 1. Introduction
References
Chapter 2. Basics of Scalar Random Processes
2.1. Basic statistical characteristics
2.2 Deterministic process
2.3 Random Process
2.4 Covariance and correlation functions
2.5 Spectral density
2.6 Examples of geophysical time series and their statistics
References
Chapter 3. Time and Frequency Domain Models of Scalar Time Series
3.1 Nonparametric spectral analysis
3.2 Parametric models of time series
3.3 Parametric spectral analysis
3.4 Determining the order of autoregressive models
3.5. Comparison of autoregressive and nonparametric spectral estimates
3.6 Advantages and disadvantages of autoregressive analysis (scalar case)
References
Chapter 4. Practical Analysis of Time Series4.1 Selecting the sampling interval
4.2 Linear trend and its analysis
4.3 Testing for stationarity and ergodicity
4.4 Linear filtering
4.5 Frequency resolution of autoregressive spectral analysis
4.6 Example of AR analysis in time and frequency domains
Appendix
References
Chapter 5. Stochastic models and spectra of climatic and related time series
5.1 Properties of climate indices5.2 Properties of time series of spatially averaged surface temperature
5.3. Quasi-Biennial Oscillation
5.4 Other oscillations
Appendix
References
Chapter 6. Statistical Forecasting of Geophysical Processes
6.1 General remarks
6.2 Method of extrapolation
6.2 Example 1. Global annual temperature
6.3 Example 2. Quasi-Biennial Oscillation
6.4 Example 3. ENSO components
6.5 Example 4. Madden-Julian Oscillation
Appendix
References
Chapter 7. Bivariate Time Series Analysis
7.1 Elements of bivariate time series analysis
7.2 Granger causality and feedback
7.3 On properties of software for analysis of multivariate time series
References
Chapter 8. Teleconnection Research and Bivariate Extrapolation
8.1 Example 1. The ENSO Teleconnection
8.2. Example 2. Teleconnections between ENSO and AST
8.3. Example 3. Bivariate Extrapolation of Madden-Julian Oscillation
Appendix
References
Chapter 9. Reconstruction of Time Series
9.1 Introduction
9.2. Methods of Reconstruction
9.3. Verification of the autoregressive reconstruction method
9.4. Discussion and conclusions
References
Chapter 10. Frequency domain structure and feedbacks in QBO time series
References
Chapter 11. Verification of General Circulation Models
11.1 Verifying the structure of ENSO
11.2 Verification of ENSO influence upon global temperature
11.3 Verifications of properties of surface temperature over CONUS
11.4. Conclusions
Chapter 12. Applications to proxy data
12.1 Introduction
12.2. Greenland Ice Cores
12.3. Antarctic ice cores
12.3 Discussion and conclusions
References
Chapter 13. Application to Sunspot Numbers and Total Solar Irradiance
13.1 Introduction
13.2 Properties of sunspot number time series
13.3 Properties of total solar irradiance time series
References
Chapter 14. Multivariate time and frequency domain analysis
14.1 Time domain analysis
14.2 Frequency domain analysis
14.3. Analysis of a simulated trivariate time series
14.4 Analysis of climatic time series
References
Chapter 15. Summary and Recommendations
References
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