Lecture Notes

The lecture notes for this course are from two different sources:  Prof. Wunsch's primer on Time Series Analysis and his forthcoming book Discrete Inverse and State Estimation Problems: With Geophysical Fluid Applications. Cambridge, UK: Cambridge University Press, 2006.  ISBN: 9780521854245. Table of contents (PDF).

Time Series Analysis: A Heuristic Primer

Table of Contents (PDF)

Preface (PDF)

Chapter 1 - Frequency Domain Formulation (PDF - 1.4 MB)

1.1 Fourier Transforms and Delta Functions (PDF)

1.2 Fourier Series and Time-Limited Functions (PDF)

1.3 The Sampling Theorem (PDF)

1.4 Discrete Observations (PDF)

1.5 Aliasing (PDF)

1.6 Discrete Fourier Analysis (PDF)

1.7 Identities and Difference Equations (PDF)

1.8 Circular Convolution (PDF)

1.9 Fourier Series as Least-Squares (PDF)

1.10 Stochastic Processes (PDF)

1.11 Spectral Estimation (PDF)

1.12 The Blackman-Tukey Method (PDF)

1.13 Colored Processes (PDF)

1.14 The Multitaper Idea (PDF)

1.15 Spectral Peaks (PDF)

1.16 Spectrograms (PDF)

1.17 Effects of Timing Errors (PDF)

1.18 Cross-Spectra and Coherence (PDF)

1.19 Simulation (PDF)

Chapter 2 - Time Domain Methods (PDF)

2.1 Representations-1 (PDF)

2.2 Geometric Interpretation (PDF)

2.3 Representations-2 (PDF)

2.4 Spectral Estimation from ARMA Forms (PDF)

2.5 Karhunen-Loève Theorem and Singular Spectrum Analysis (PDF)

2.6 Wiener and Kalman Filters (PDF)

2.7 Gauss-Markov Theorem (PDF)

2.8 Trend Determination (PDF)

2.9 EOFs, SVD (PDF)

Chapter 3 - Examples of Applications in Climate (PDF)

3.1 References (PDF)