GO TO Graduate Mathematics Courses Page GO TO Mathematics and Statistics Home Page Beyond the Catalog: Notes or Advice Course Description: This course is intended to present the basis
models, methods and concepts of time
series analysis to students with a good background of intermediate mathematical
statistics. Some elementary knowledge of basic linear regression analysis would
also be helpful. The presentation will be balanced between theory and data
analysis, with sufficient theory to understand the basis of the methods and
models. Case studies will be drawn from business and economics, engineering,
meteorology, etc., and data will be analyzed by students using existing
computer programs (Minitab and SAS).
Topics to be covered may include stationary stochastic
processes, autocorrelation,
partial autocorrelation, representation of dynamic relations by difference
equations, AutoRegressive Integrated Moving Average (ARIMA) models, structural
component models, identification of models, estimation and diagnostic checking
of time series models, model selection procedures, tests for (unit root)
nostationarity, noninvertibility, seasonal models, theory of prediction and
forecasting, elements of spectral analysis, time series regression analysis
with autocorrelated errors, dynamic regression models and transfer function
models, intervention analysis models and outlier detection, linear filters
and their spectral properties, state-space model forms and Kalman filtering
and smoothing methods, nonlinear and (AutoRegressive) Conditional
Heteroskedastic (ARCH) time series models, and long memory and fractional
ARIMA models. Due to time constraints, not all the latter topics mentioned
will be covered in the course.
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None.
This course is prerequisite to the following courses: