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Lecture Notes

Wunsch, Carl. Time Series Analysis, A Heuristic Primer. (Available by chapter below)

Contents

  1. 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

  2. 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

  3. 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)