GOV 385L • Time-Series Analysis
3:00 PM-6:00 PM
I will present a number of topics central to the study of time series that is central to the art and science of statistical time series analysis. I will present lectures based on my notes. When appropriate I will relate my presentation with the exposition in Spectral Analysis and Time Series, Maurice Priestley, Academic Press. I will tailor the course to the background and need of the graduate students who will take the course. I will attempt to keep the mathematical level as simple as possible. I will present the mathematics that I need. Students are required to know basic linear algebra and the basics of statistical methods.
Course Topics 1. Basic ideas of statistical reasoning 2. Fundamentals of probability at an elementary level 3. Linear homogeneous differential & difference equations a. Characteristic equation 4. Linear systems a. Matrix representation of any difference equation b. General solution in terms of eigenvalues 5. Sampling a signal a. Aliasing as an identification problem 6. Basics of stochastic processes a. Stationarity b. Ergodicity & mixing c. Discrete example of the "curse of dimensionality" 7. Autoregressive processes (AR) 8. Moving average processes (MA) a. Invertibility 9. Vector autoregressive models (VAR) a. Estimating the parameters of a VAR b. Forecasting a few steps ahead 10. Trends and unit roots 11. Fourier transform a. The spectrum b. Time-frequency relationships for linear systems c. Cumulants and cumulant spectra 12. Nonlinear processes
Any person taking the course for credit must write a paper on any research project of interest to the student. The paper must address some aspect of time series analysis no matter how simple. I will distribute several time series programs via e-mail attachments. I will demonstrate the programs in class.
Priestley, Maurice. Spectral Analysis and Time Series. Academic Press.