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Lecture notes. Written from the material of Berkeley Stat 153, licensed CC BY 4.0. Notes, not a transcript — reorganised and rewritten, carrying the same licence.

Berkeley Stat 153

128 chapters, written from the course's material.

Contents

  1. White Noise and Random Walks
  2. Mean, Autocovariance, and Correlation
  3. Autocovariance and Stationarity
  4. Linear Regression for Time Series
  5. OLS and MLE in Regression
  6. Simple and Multiple Linear Regression
  7. Sinusoidal Nonlinear Regression
  8. Improving upon the linear model
  9. Cross-Validation and Regularization
  10. Periodic Signals and the Periodogram
  11. Fourier Transform and Spectral Density
  12. Smoothing the Periodogram (part 1)
  13. Time-Frequency Analysis of Music
  14. Intro to Autoregressive Models
  15. Autoregressive Moving Average Models
  16. Identifying ARMA Models via ACF/PACF
  17. Fitting and Diagnosing ARIMA Models
  18. Time-Lagged Regression and the STRF
  19. State Space Models
  20. The Kalman Filter and Smoother
  21. Convolutional Networks and Discrete Convolution
  22. Building Blocks of Convolutional Networks
  23. Recurrent Neural Networks
  24. Gated RNNs: LSTMs and GRUs
  25. From Sinusoid to AR(2)
  26. AR Fitting: AutoReg vs ARIMA
  27. High-Dimensional Regression for Change-Points
  28. Change-Point Detection and Estimation
  29. AR(p): Levels, Logs, and Differences
  30. Fitting Trends to Time Series
  31. Causal Stationary AR(2) Example
  32. Scaling and Initialization in PyTorch
  33. Inference in Sinusoid Models
  34. Estimating MA(1) Parameters
  35. Anatomy of a Regression Fit (part 1)
  36. The Periodogram and Sinusoidal Models
  37. AR(p) Forecasting and Prediction Uncertainty
  38. Ridge and LASSO Trend Estimation
  39. Applying the Spectrum Smoother
  40. Regression Uncertainty and Profile Estimation
  41. Time Series Regression and Uncertainty
  42. Smoothing Trend, Variance, and Spectrum
  43. Multiple Sinusoids and Change-Points
  44. Prediction Uncertainty in AR Models
  45. Sinusoidal Regression and the DFT
  46. AR(p) Estimation and Forecasting (part 1)
  47. Profile RSS: Changepoints and the Periodogram
  48. Autoregressive Models in Practice
  49. Broken-Stick Regression and Regularization
  50. Bayesian Regularization and Variance Models
  51. Trend and Seasonal Regression
  52. Bayesian Regularization of Trends
  53. ACF, PACF, and AR(p) Stationarity
  54. Nonlinear Autoregression and Overfitting
  55. Model Fitting via PyTorch
  56. Identifying and Fitting ARIMA Models
  57. LSTM Networks for Forecasting
  58. Multiplicative Seasonal ARMA Models
  59. ARMA and ARIMA Model Identification
  60. Regression for Time Series Trends
  61. The Discrete Fourier Transform
  62. AR(p) Estimation and Multistep Forecasting
  63. Ridge and Lasso Trend Filtering
  64. Posterior of Multiple Regression Coefficients
  65. Frequentist and Bayesian Regression Inference
  66. Frequency and Breakpoint Estimation
  67. Regression with an Unknown Changepoint
  68. Autoregression and Yule's AR(2)
  69. Bayesian Shrinkage and Variance Models
  70. Bayesian Reasoning for Noisy Measurements
  71. Ridge Regression as Bayesian Inference
  72. Stationary MA and AR Processes
  73. \(MA(q)\) models
  74. Neural Network Models for Time Series
  75. Multiplicative Seasonal ARIMA Models
  76. ARMA and ARIMA Models
  77. Homework Assignments Index
  78. Correlation, Random Walks, and Stationarity
  79. Regression: Estimation and Evaluation
  80. Homework 3
  81. Long-Range ARIMA and Cross-Validation
  82. Evaluating Covid-19 Death Forecasts
  83. Course Overview: Time Series Analysis
  84. Fitting AR(p) Models to GNP
  85. ACF and PACF in Practice
  86. ARIMA Fitting and Model Selection
  87. Change-of-Slope Regression and Scaling
  88. Fitting MA(1)/AR(1) via PyTorch
  89. LSTM Forecasting for Time Series
  90. Change of Variables and MLE
  91. Anatomy of a Regression Fit (part 2)
  92. Frequency Estimation and Aliasing
  93. Inference in Nonlinear Regression Models
  94. Change-point model
  95. High-dimensional regression for change-points
  96. Smoothing the Periodogram (part 2)
  97. Sinusoid, Yule, and AR(2) Models
  98. Discrete Fourier Transform and Periodogram
  99. AR(p) Estimation and Forecasting (part 2)
  100. Ridge and LASSO Trend Filtering
  101. Smoothing the Periodogram (part 3)
  102. The Posterior t-Distribution in Regression
  103. Frequentist and Bayesian Linear Regression
  104. Mean, Variance, and Spectrum Models
  105. Multiple Frequencies and Change-of-Slope Models
  106. Introduction to Time Series (part 1)
  107. Introduction to Time Series (part 2)
  108. Introduction to Time Series Analysis
  109. The Sinusoidal Model
  110. Parameter Estimation in AR(1)
  111. Broken-Stick Regression
  112. AR Models and Sunspots
  113. High-Dimensional Regression and Regularization
  114. Sinusoidal Models for Sunspots
  115. Bayesian Priors and Least Squares
  116. Bayesian View of Ridge Regression
  117. MA Models and AR(p) Stationarity
  118. Nonlinear Autoregression
  119. From Regression to RNNs
  120. Stationarity and Causality of AR(p)
  121. From AR to LSTM
  122. Box-Jenkins Strategy and SARIMA Models
  123. Stationary Solutions of AR(p)
  124. Simple Linear Regression
  125. Evaluating Forecasting Hub Performance
  126. Supplementary Reading List
  127. Stat 153 Course Syllabus
  128. Finger Tapping Regression Exercise

Sources

5 course offerings were merged. The book carries CC BY 4.0.

Offering Original Commit Licence
Fall 2024 github.com/berkeley-stat153/fall-2024 94c943d CC BY 4.0
Spring 2025 github.com/berkeley-stat153/spring-2025 60232ff CC BY 4.0
Fall 2025 github.com/berkeley-stat153/fall-2025 df8e8e9 CC BY 4.0
Spring 2026 github.com/berkeley-stat153/spring-2026 c08dd12 CC BY 4.0
Fall 2026 github.com/berkeley-stat153/fall-2026 1df2e36 CC BY 4.0