Stat429syllabus 2017 PDF

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THE UNIVERSITY OF ILLINOIS Department of Statistics STATISTICS 429 Time Series Analysis Fall 2017 Instructor information: Xiaofeng Shao, Ph.D. Professor 113C Illini Hall Webpage: http://publish.illinois.edu/xshao/ Office hours: Friday (1.30-3pm) and by appointments. Teaching assistant information: Runmin Wang, Ph.D. student, [email protected] Discussion and Office Hours: Wednesday 2-4pm, Illini Hall 122/104. Required Textbook: Shumway and Stoffer. (2016) Time Series Analysis and Its Applications, with R examples, 4th edition. Major Reference Books: 1. Hamilton, J. D. (1994) Time Series Analysis. Princeton University Press. 2. Brockwell and Davis. (1991) Time Series: Theory and Methods, 2nd edition. Software: R Project which can be downloaded at http://www.r-project.org R codes and datasets: http://www.stat.pitt.edu/stoffer/tsa4/ Pre-requisites: STAT410. In particular the students should be familiar with the following concepts: conditional probability, distribution of random variables, first and second order moments, sampling distributions, central limit theorem, maximum likelihood estimation and hypothesis testing, linear regression and analysis of variance. Course content Part I: Chapters 1 ,2, 3. • • • • • • • •

Objective of time series analysis and examples of time series data sets Time series models Stationarity, autocovariance, autocorrelation MA, AR, and linear processes Sample ACF and its properties, its connections to forecasting Estimation of µ and related large sample theory. Causality, invertibility, and AR(p) models. ARMA(p, q) models and their properties 1

• Linear prediction, partial ACF • Forecasting stationary time series. Part II: Chapter 3 • • • •

Parameter estimation: Yule-Walker estimation, MLE Order Selection, Model diagnostics and ARIMA models. Seasonal ARMA models. Classical decomposition of time series data, estimation of the trend and seasonality Part III: Optional topics (Chapters 4,5)

• • • •

Spectral analysis of time series Long memory time series GARCH models Multivariate time series

Grading: 1. One midterm exam (25%) and final exam (45%), 4-6 problem sets (combined for 30%). The final exam may have two parts: in-class exam and a take-home project. A takehome project will involve analyzing real data sets and writing a report. 2. (Rough) Scale: A : [90, 100]; B : [80, 90); C : [70, 80); D : [60, 70); F : [0, 60). 3. A grade of A+ will be awarded to the student whose average is at least 98% and has the highest average in the class. Notes: 1. All exams are cumulative. 2. No special make up exam is given for any of the exams that are missed except for extreme health problems. Proper documentation should be provided (e.g. a doctor’s certificate ordering you to stay in the hospital or at home). 3. Problem sets must be handed at the beginning of the lecture on the day that they are due. Late problem sets cannot be accepted. 4. Discussion of homework problems is encouraged, but solutions must be written up individually. Direct copying is not acceptable. 5. If there is an error in the homework or exam grading, you need to contact Runmin or me right after the homework or exam paper is returned. The grade won’t be changed if it is beyond one week. 2

6. If you want to ask questions about this course during my office hour, please knock in. For other time, please send me an email beforehand and make an appointment. Problem Set 1 (incomplete). I will update the problem set after each class. Due date will be announced at least one week ahead. You are required to do all the listed problems but only a few will be selected for grading. Show all solutions explicitly. • Chapter 1: 1.2 Tentative Exam Dates Midterm 1: around Oct 17-19, 2017. Final: 8:00-11:00 a.m., Tuesday, December 19 2017. The date is set by the university.

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