STAT 481/581: INTRODUCTION TO TIME SERIES ANALYSIS

Department of Mathematics and Statistics.
University of New Mexico.


Fall Semester 2008


Instructor: Gabriel Huerta Office: 441 Humanities Building.
email: ghuerta@stat.unm.edu Phone: 277-2564
Class Time: T R 14:00-15:15 Classroom : Mitchell Hall 120
Office hours: T R 11:00-13:00 or by appointment
Webpage: http://www.stat.unm.edu/~ghuerta/tseries/stat581.html

  • Handouts and class notes
  • Homeworks
  • Data sets
  • Research papers in Time series
    • Class Description
    This class offers an introduction to time series methods from both a theoretical and applied perspectives. Topics to be discussed in this class are exploratory techniques for time series (autocorrelations, periodogram, etc.); spectral theory and estimation; Autoregressive Moving Average (ARMA) models; Box-Jenkins methodology; forecasting in time series; diagnostics of time series models. Special topics may consider Bayesian approaches, state space models, ARCH-GARCH models. The methodology will be illustrated with the analysis of different data sets arising in the context of the physical sciences, psychology, economics and finance, etc.
    Prerrequistes
    Probability (STAT 461/561). Previous experience with linear regression (STAT 440/540) and statistical computing is a plus but not required.
    Program
    This course covers the following aspects in time series: exploratory methods, analysis in the frequency and time domains, modeling for stationary processes. Mainly topics for univariate time series will be discussed in this class. This is how I expect the course to develop:

  • Introduction to time series and exploratory techniques. Time plots, calculation of the sample autocorrelation. (Class Notes. Shumway and Stoffer Ch. 1 and 2)
  • Time Series Regression (Class Notes. Shumway and Stoffer Ch. 2)
  • ARMA modeling. Estimation of autoregressive moving averages processes via frequentist and Bayesian approaches. Model diagnostics, forecasting and applications. (Class Notes. Shumway and Stoffer Ch. 3)
  • Spectral estimation using Fourier analysis and Filtering. Bayesian Approach (Class Notes. Shumway and Stoffer Ch. 4)
  • Special topic: Non-stationary time series processes. State Space Models. Bayesian Approach ( Class Notes, Shumway and Stoffer Ch. 6)
  • Special topic: Long memory, GARCH, treshold models. (Shumway and Stoffer Ch. 5)
    Data sets
    One of the main goals of this course is to familiarize the student with different methods for time series through analyzing different data sets. Some of the data that we will study are related to:

  • climatology issues involving warming trends.
  • inference on periodicities for light intensity of variable stars.
  • study of trends for ozone series at urban and rural areas.
  • changes in economic behavior and financial settings.
    • Computing
    I will provide code in R for the different methods discussed in class, although the material is not R-dependent. Matlab can be used as alternative to R or Splus. SAS and SPSS can be used for exploratory analysis and to fit ARIMA models. The R software is free and available at:
  • R software
    • For those of you using R for the first time, I recommend you read Introduction to R document available from the Manuals section of R.
    Class Materials
  • I will provide some Latex class notes through this web-page. Also, I will provide R code with examples.
  • The main text for this course is the second edition of the book: Shumway, R.H. and Stoffer, D.S. (2006) Time Series Analysis and its Applications with R Examples Springer Verlag (2nd edition). The data files and R code for this text are available at:
  • Data files text
    • Other textbooks in time series are:
  • Chatfield, C. (2004) The Analysis of Time Series: An Introduction Chapman and Hall (6th edition).
  • Box, G.E.P, Jenkins, G. and Reinsel, G. (1994), Time Series Analysis Prentice Hall (3rd. edition).
  • Diggle, P. (1990) Time Series: A Biostatistical Introduction Oxford University Press.
  • West, M. and Harrison, P.J. (1997), Bayesian Forecasting and Dynamic Models , Springer-Verlag, (2nd Edition)
  • Pole A., West M. and Harrison P.J. (1994), Applied Bayesian Forecasting and Time Series Analysis . Chapman-Hall.
    Grading
  • Homework assignments. 50%
  • Final project (may include a short presentation) 50%