Wunsch, Carl. Time Series Analysis, A Heuristic Primer. (Available by chapter below)
Contents
- Frequency Domain Formulation (PDF 1 of 4) (PDF 2 of 4 - 2.9 MB) (PDF 3 of 4) (PDF 4 of 4 - 1.9 MB)
1.1 Fourier Transforms and Delta Functions
1.2 Fourier Series and Time-Limited Functions
1.3 The Sampling Theorem
1.4 Discrete Observations
1.5 Aliasing
1.6 Discrete Fourier Analysis
1.7 Identities and Difference Equations
1.8 Circular Convolution
1.9 Fourier Series as Least-Squares
1.10 Stochastic Processes
1.11 Spectral Estimation
1.12 The Blackman-Tukey Method
1.13 Colored Processes
1.14 The Multitaper Idea
1.15 Spectral Peaks
1.16 Spectrograms
1.17 Effects of Timing Errors
1.18 Cross-Spectra and Coherence
1.19 Simulation
- Time Domain Methods (PDF - 1.6 MB)
2.1 Representations-1
2.2 Geometric Interpretation
2.3 Representations-2
2.4 Spectral Estimation from ARMA Forms
2.5 Karhunen-Loève Theorem and Singular Spectrum Analysis
2.6 Wiener and Kalman Filters
2.7 Gauss-Markov Theorem
2.8 Trend Determination
2.9 EOFs, SVD
2.10 References
- Examples in Climate Change (PDF - 2.1 MB)
3.1 Gravitational Tides
3.2 Thermal Tides
3.3 The Milankovitch Problem
3.4 Analysis
3.5 Detection of Non-Linearities
3.6 Introduction
3.7 Obtaining a Precessional Period-Rectification
3.8 A Potential Positive Aspect
There are also corrections, additions and exercises (PDF)