Key Features 

• Explore edge cases and deepen conceptual understanding

• Debug R code with real-time guidance

• Learn fundamental time series topics, including: stationarity, autocorrelation, spectral analysis, filtering and forecasting

• Gain exposure to non‑standard concepts such as: entropy, volatility filtering and time series bootstraps

• Benefit from a blend of conceptual learning, author‑led coding, and live Q&A

• Experience a practical, engaging, and accessible format ideal for those new to time series

This short course series will cover the content of the book Time Series: A First Course with Bootstrap Starter in twelve sessions, each session covering a chapter. The course will be delivered to the National Institute of Statistical Sciences (NISS). The intended audience includes statisticians with little or no knowledge of time series, but a general knowledge of statistics. Prerequisites include a course on linear models, a course on mathematical statistics (such concepts as bias, variance, and the Gaussian distribution), and a familiarity with linear algebra (the transpose, inverse, and eigen-values of a matrix). The aim is to cover basic concepts of time series analysis at a level suitable for those with a bachelor's or master's degree in statistics, while including a few non-standard concepts such as entropy, volatility filtering, and time series bootstraps. A second aim is to incorporate coding in R of all concepts, methods, and examples. 

 

VIsit Full Course Syllabus: GitHub - tuckermcelroy/BEwebinar: Materials for ASA Webinar sponsored by Business and Economics Section

 

The course will emphasize the methodological and computational aspects of the book's material. While the course will not include proofs, some important theoretical results will be discussed. The following outline provides the main topics; in italics are topics not typically covered in a time series course.

1. Introduction: time series data, cycles, regression, and autoregression
2. Stochastic Processes: stationarity, autocovariance, moving averages, white noise, and integrated processes
3. Filtering: linear filters, trends, and seasonality
4. Forecasting: prediction, normal equations, and iterative forecasting
5. ARMA: ARMA recursion, difference equations, and autocovariance generating functions
6. Frequency Domain: spectral density, frequency response functions, inverse autocovariances, and partial autocorrelations
7. Frequency Domain: discrete Fourier Transform, optimal filtering, Wold decomposition, and cepstrum
8. Model Identification: maximum entropy, time series entropy, and Kullback-Leibler discrepancy
9. Statistical Estimation: sample mean, sample autocovariance, spectral mean, and periodogram
10. Model Fitting: Gaussian likelihood, fitting AR and MA models, model assessment, and AIC
11. Nonlinear Time Series: GARCH processes, bi-spectral density, and volatility filtering
12. The Bootstrap: Monte Carlo, plug-in principle, model-based bootstrap, sieve bootstraps, subsampling, block bootstrap, stationary bootstrap, and model-free bootstrap

The teaching format is live and virtual. Webinars will be held weekly for one hour, with instruction being offered in real-time. The course will utilize R notebooks associated with the textbook. Each notebook corresponds to a lesson, covering a few examples or one concept, and occupying 5-10 minutes of time. Each one-hour webinar will cover 4-9 notebooks. The teacher will review that material in the lesson, explaining the main concepts. Students can execute the code on their own laptop, and then during instruction the instructor may modify the code; students can follow along and modify the code, or rewrite it, and in real-time see the new results. The notebooks are freely available on the Github site.

1. Time Series Data
2. Cycles
3. Windows and Transforms
4. Regression and Autoregression

1. Random Vectors
2. Stochastic Processes
3. Stationarity
4. Autocovariance
5. Autoregression and Moving Average
6. White Noise Processes

1. Nonparametric Smoothing
2. Linear Filters
3. Examples of Filters
4. Trends
5. Seasonality
6. Trend and Seasonality
7. Integrated Processes

1. Vector Space Geometry
2. The L2 Space
3. Projection in Hilbert Space
4. Time Series Prediction
5. Linear Prediction
6. Orthonormal Sets
7. Projection of Signals

1. ARMA Recursion
2. Difference Equations
3. Causality of AR(1)
4. Causality of ARMA
5. Invertibility of ARMA
6. Autocovariance Generating Function
7. MA Representation
8. Recursive Computation of Autocovariance

1. Spectral Density
2. Filtering in Frequency Domain
3. Inverse Autocovariance
4. Toeplitz Matrices
5. Partial Autocorrelation
6. AR and MA Identification

1. Herglotz Theorem
2. Discrete Fourier Transform
3. Spectral Representation
4. Optimal Filtering
5. Kolmogorov's Formula
6. Wold Decomposition
7. Cepstrum

1. Introduction to Entropy
2. Entropy Mixing
3. Maximum Entropy
4. Time Series Entropy
5. Markov Time Series
6. Modeling via Entropy
7. Kullback-Leibler Discrepancy

1. Weak Dependence
2. Sample Mean
3. Serial Correlation
4. Sample Autocovariance
5. Spectral Means
6. Periodogram
7. Spectral Density Estimation
8. Spectral Analysis

1. MA Identification
2. AR Identification
3. Optimal Prediction Estimators
4. Relative Entropy Minimization
5. Computation of Optimal Predictors
6. The Gaussian Likelihood
7. Model Assessment

1. Information Criteria
2. Model Comparisons
3. Iterative Forecasting
4. Imputation and Signal Extraction
5. Nonlinear Processes
6. ARCH Process
7. GARCH Process
8. Bi-spectral Density
9. Volatility Filtering

1. Sampling Distributions
2. Monte Carlo
3. The Plug-in Principle and the Bootstrap
4. Model-based Bootstrap
5. Sieve Bootstraps
6. Time Frequency Toggle Bootstrap
7. Subsampling
8. Block Bootstrap

Students will obtain a basic knowledge of time series theory and methodology. They will be able to analyze time series data by exploratory analysis, by model identification and fitting, and by making applications such as forecasting. Students will know how to use R to perform these tasks: not only to apply common time series functions appropriately, but also to write R scripts that capture time series methodology. In addition to learning basic time series topics, including ARMA modeling, students will learn how to use entropy, frequency domain methods, and time series bootstraps.

The course will be drawn from the textbook's material, but presentations will be primarily rendered through R Notebooks. The instructional strategy will be to briefly discuss a new topic, and then demonstrate through R code the computational and empirical facets of the topic. Short exercises can then be given, where the teacher asks the students to modify the R code to generate a different result. Through the technology of the virtual format, the instruction can be paused to address student questions.