STA 642
Time Series & Dynamic Models

Here is the latest semester STA 642 Web Site for registered students

Synopsis: This graduate course concerns models and methods for time series, covering a broad class of dynamic models (a.k.a. state space models) for univariate series, with special cases including autoregression and time-varying autoregressions as well as non-stationary models for trends, seasonality and dynamic regression, and stochastic volatility. Core aspects concern model structures, Bayesian analysis for filtering and forecasting, time series decomposition in dynamic models, model monitoring and structure assessment. Topics include dynamic models for discrete (count) time series forecasting as well as conditionally Gaussian models. The course builds on the foundation in univariate modelling to explore multivariate time series analysis and forecasting, selecting from a range of multivariate model structures. Student will routinely code for class and homework examples, with data drawn from areas such as economics, finance, commerce, IT, neuroscience, climatology, and others.

Prerequisites: This graduate course in Statistical Science builds on advanced preparation in statistics including Duke STA courses 601/602 (critical) & 523, as well as 532 (co-reg is OK); then, background in the material covered in 531 (or 831) is highly desirable. These courses define basic preparation in core theory of stochastic processes, theory and methods of Bayesian modelling and inference, and Bayesian computation using a range of simulation-based methods. Students need to be ready in these terms.

See more detailed prereqs and expectations of prior preparation below

Registration: Hardwired prerequisites and/or instructor permission required.

Graduate credit units: 3

Assignments and Assessment:

  • Extensive reading, working derivations, coding examples
  • Regular homeworks
  • Regular class participation and engagement
  • Midterm and final exams

Texts & Reading:

  • Course text: Time Series: Modeling, Computation, and Inference (2nd edition), by Raquel Prado, Marco Ferreira & Mike West, 2021, Chapman Hall/CRC Press Taylor & Francis Group.
  • Key support text: Bayesian Forecasting & Dynamic Models (2nd edition), by Mike West & Jeff Harrison, 1997, Springer-Verlag.
  • Additional materials provided by instructor-- supplementary course notes, copious course slides and support code. Additional reading may be added.

Code & Data: Students will be expected to develop computational algorithms and exploratory modelling exercises with minimal supervision-- all to support student learning based on replicating, redeveloping and extending class examples (and going beyond). Copious Matlab support code and examples are provided, with much explored in-class and through homeworks. Students will develop their own custom code for homework exercises, general learning and final exam assignments. Students may, of course, use R, python or other computing environments/languages, but the course examples and support use (only) Matlab.

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STA 642: Key background and proficiency in the following technical topics is assumed.

  • Routine facility in manipulations of standard univariate and multivariate distributions-- derivation of conditional and marginal distributions from multivariate models, matrix/vector analysis for means and covariances, Jacobian-based transformations.
  • Facility in manipulation of likelihood functions, priors and posteriors in conjugate analysis in standard models, and multiple linear regression including normal/inverse gamma theory. Notation of linear models and associated distributions, and linear algebra associated with these models and theory. Knowledge of basic aspects of multivariate normal/inverse Wishart distributions and some of their uses.
  • Exposure to Bayesian simulation-based methods of computation including direct simulation of distributions (using compositional sampling in multivariate contexts) and with MCMC methods for posterior inference. At that introductory and practical level, students will have encountered key stochastic process concepts including Markov process models, stationarity, autocorrelation, and convergence of realizations of Markov process to stationary distributions.
  • Routine facility in linear algebra: manipulation of multivariate distribution theory in vector/matrix derivations; eigenvectors/eigenvalues of square matrices and their special cases in PCA with (symmetric positive definite) variance matrices.
  • Some exposure to manipulation of complex numbers-- complex eigenvalues arise frequently in eigendecompositions of matrices in many statistical models, and particularly in Markov state-space models. This is relevant to understanding and manipulation of central classes of dynamic models in applied forecasting and time series analysis-- traditional stationary models as well as central classes of non-stationary models.
  • Matlab: while prior experience in Matlab is not necessary and it is not required ... the course uses Matlab exclusively and provides very extensive code (examples, support and utility functions) for in-class examples, for students to explore as part of the learning process, to use and develop in homeworks and exams. Any student without a working familiarity in Matlab is (strongly) advised to spend time in advance developing expertise. A student can code in R or other languages, but there will be no support for other than Matlab.