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)

Course Info

Learning Resource Types

assignment Problem Sets
assignment Programming Assignments
notes Lecture Notes