Syllabus

Course Description:

An introduction to time series analysis in the time domain and spectral domain. Topics will include: estimation of trends and seasonal effects, autoregressive moving average models, forecasting, indicators, Fourier analysis, spectra, wavelets, state-space models, filtering and smoothing.

Prerequisites:

Stat 101, Stat 134 or consent of instructor.

Textbook:

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

Course Format:

Three hours of lecture (MWF 11:00, 3111 Echeverry) and two hours of laboratory per week.

Homework

There will be weekly homework assignments, due one week after being passed out. Late homeworks will not be accepted.
You should try to solve problems on your own. If you discuss problems with another student, indicate on your writeup the name of your collaborator(s). In any case you must write up your own solutions.

Grading

There will be a midterm exam and a final exam. The midterm will count 25% of your grade, and the final 35%. Homework will count 20% and labs will count 20%.

Principal Topics

  • stationary processes---mean and autocovariance function
  • forecasting---the Durbin-Levinson and innovations algorithms
  • ARMA models
  • spectral analysis---spectral densities, the periodogram, windowing
  • estimation---Yule-Walker, innovations, maximum likelihood
  • estimation and forecasting
  • trends and seasonality
  • order selection---FPE, AICC
  • nonstationarity---ARIMA models
  • state-space models
  • wavelets
  • nonlinear models