Statistics 730   Time Series Analysis

Spring 2026MWF 9-9:50, Room PHYS 2214

Instructor: Eric Slud, Statistics Program, Math. Dept.    Office:  Mth 2314, x5-5469,     email slud@umd.edu

Office Hours (initially): Monday 10-11, Fri 11-12 or by appointment (email me!)

If you have any issues with accessibility of this web-page and course materials -- please inform the course instructor, so that these issues can be addressed.

Syllabus Lecture & Computing Handouts Homework

For a set of Sample Problems for the In-Class Test, click here.

Required Course Text: 
R. Shumway & D. Stoffer, Time Series Analysis and its Applications, 2006 2nd ed. or later, Springer.
(The 2006 Second Edition is free as an e-book to UMCP students through the library: see website with datasets and errata.)

Recommended text: H. Lutkepohl, New Introduction to Multiple Time Series Analysis, 2005, Springer. (Also free as e-book.)

Overview: This course covers the concepts and tools of statistical time series analysis, both from a mathematical and a data-analytic viewpoint. Course segments on mathematical tools will be interleaved with segments emphasizing model-building, statistical analysis (in R), and simulation. The course introduces methods both in the time and frequency domains. The mathematical theorems and proofs are an essential part of the course. Students will be required to make further mathematical arguments and extensions in graded homework problems, and understanding of the conditions under which the techniques are valid will be tested.

Prerequisite: Stat 700 plus a graduate course in mathematical analysis, plus some computing familiarity.

Course requirements and Grading: there will be 6 or 7 graded homework sets (one every 1 to 2 weeks) which together will count 1/3 of the course grade. There will also be an in-class test and a final course project (or take-home test), each of which will count as 1/3 of the course grade.

NOTE ON USE OF THEORETICAL MATERIAL.  Both in homeworks and the in-class test, there will be theoretical material involving probability theory as needed to apply the law of large numbers and central limit theorem, along with the `delta method' (Taylor linearization), linear algebra and other manipulations at advanced-calculus level, in some cases verging on measure-theoretic probability techniques. (Look at Appendix A of the Shumway-Stoffer book for the flavor and level.). There will also be some use of Hilbert space methods. The theoretical material in the Shumway and Stoffer book is concentrated in the Appendices, but that material will be supplemented in class.

Course Coverage: Chapters 1-5 and Appendixes A, B, C Shumway-Stoffer, plus some material from Chapters 6-7 and from Lutkepohl Chapters 2--3 as time permits.

NOTE ON COMPUTING.  Both in the homework-sets and the course project, you will be required to do computations on real datasets using a statistical-computing platform such as R or SAS or MATLAB. The book and various class demonstrations and scripts on this web-page will be given in R, and that is the only software platform that I will use or provide help with. If you are learning one of these packages for the first time, I strongly recommend R, and I will provide links to free online materials introducing them. In addition, there is a concise introduction to R commands in time series analysis that you should consult. R is freely available in Unix or PC form through this link. For the systematic Introduction to R and R reference manual distributed with the R software, either download from the R website or simply invoke the command

> help.start()

from within R. For a quick start, see my own Rbasics handout originally intended for a Survival Analysis class, and then read more about R objects and syntax in the Venables and Ripley text, in my Stat 705 Lecture Notes, and in the R introduction manual distributed with the R software. A really useful short summary of a lot of R commands can be found here. See also the previously mentioned concise introduction to R commands in time series analysis .

R Logs

For R practice logs that will periodically illustrate R commands related to time series data and exercises, see RLogsS730 Directory.

Lecture-Topic Handouts

(I) Lecture1 Slides .

Homework problems for 2026.

Assignment 1. (First 2 weeks of course, HW with 6 Problems due Thurs., Feb. 12, 11:59pm on ELMS.).
Read Chapter 1 plus Section A.1 (Appendix A).
Do problems in Shumway-Stoffer 2nd or 3rd ed. #1.13, #1.14, #1.2(a) with #1.22 plus 3 other problems linked here.

SYLLABUS for Stat 730

I. Definitions and Constructions of Time Series Models. (2 weeks, Ch. 1 & Appendix A)
A. White Noise AR, MA, Random Sinusoids
i. R basics and time series commands
B. Autocovariance and autocorrelation functions.
C. Strong and Weak Stationarity
D. Review: Multivariate Normal, Convergence of RVs and Distributions, & Limit Theorems (leading to Thm A.2).

II. Exploratory Data Analysis for Time Series. (2 weeks, Ch. 2)
A. Regression and ANOVA (Gaussian case)
i. Information Criteria and Model Building
ii. Differencing
B. Autocorrelation and Spectrum Estimation (Periodogram)
C. Kernel and Spline Smoothing

III. Autoregressive Integrated Moving Average (ARIMA) Models. (5 weeks, Ch. 3 & Appendices A,B)
A. Definitions, Relation to Difference Eq'ns
i. Autocorrelation and Partial Autocorrelation
ii. Prediction; Nonstationary Models
B. Estimation, Model-building
C. Decomposition into Signal, Noise, and Seasonal Components

IV. Spectral (Fourier) Analysis & Periodogram. (4 weeks, Ch. 4 & Appendix C)
A. Filtered Series, Periodogram & Discrete Fourier Transform
B. Nonparametric vs. Parametric Spectral Estimation
C. Fourier Analysis vs. Wavelets
D. Estimation, Prediction, & Filtering
E. Extensions to Multiple (Vector) Time Series

V. Miscellaneous Topics. (2-3 weeks, Ch. 5 & 6)
A. GARCH, Long-memory and ARMAX Models
B. State Space Models & Methods
C. Likelihoods in Time-Domain and Spectral Forms, Maximum Likelihood, Missing Data, Structural Models

Project Ideas -- for a list of Project paper Guidelines, click here.

Suggestions for ideas and papers which might be used as the basis for a final report or project will be added here from time to time. The Final Project will be due by 5pm Fri., May 19.

(1) Time series methods are sometimes used in connection with repeatedly collected survey data. Two technical reports that provide good exposition of how sample survey theory and time series ideas combine are Bell & Hillmer 1987 and Bell & Hillmer 1989, and there are many later references to sample-survey data with a history of using time-series methods, such as the Current Population Survey monthly employment numbers.