Stat 6871: Graduate Time Series

Time Series Analysis is the study of correlated variables measured in time.  First, by introducing methods used to describe trends and seasonal patterns we will become familiar with time series data.  Second, the Time Domain approach will be presented.   The Time Domain approach assumes that time series data can be modeled in terms of past values of the series, this is because of autocorrelation in the data.  We will study some time domain methods such as the use of the autocorrelation function (ACF), the partial autocorrelation function (PACF), and Box-Jenkins ARIMA modeling.  Third, the Frequency Domain approach will be presented.  The Frequency Domain approach assumes that time series data can be modeled as the combination of sine and cosine waves with differing amplitudes and frequencies.  We will learn about some frequency domain methods of time series analysis such as the spectral density and input-output modeling.

The class will be split approximately equally between the discussion of the introductory theory and the application of the methods to real data.  All data analysis will be done in Splus.  Examples for the course will come from such diverse fields as Economics, Biology, Medicine, Seismology, and Engineering.

Required Text:  Brockwell, P.J. and Davis, R.A., Introduction to Time Series and Forecasting, Springer-Verlag, New York, 1996.

Recommended Texts: 

• Shumway, R., Applied Statistical Time Series Analysis.
• Box and Jenkins, Time Series Analysis, Forecasting and Control.
• Chaterfield, The Analysis of Time Series: An Introduction.

Homework:  The homework will consist of problems from the book and data analysis problems where Splus code will be given as guides.

Grading:

• Homework/Lab        25%
• Midterms                  25%
• Project                    25%
• Final                        25%          

Prerequisites: Working knowledge of Probability and Statistics at the level of Stat. 3401 and 3402, and knowledge of Linear Algebra will be assumed. 

Data:

• 500 Time Series Datasets
• Statlib

Handouts and Labs:

• Sylabus     in pdf
• Splus Introduction
• Lab1
• Lab2
• Lab3
• Lab4
• Lab5
• Lab6
• Lab7
• Lab8

Data sets for Homework 4: 

• Racife
• Securities
• Airpass

Homework Solutions:

• Homework1
• Homework2
• Homework3

Midterm Solutions:

• Midterm 1

Final:

• Final