A time series is a sequence X(1),...,X(N) observed in time. Examples include economic time series such as average monthly rate of inflation, meteorological time series such as daily maximum temperature, signature of an engin vibration observed every millisecond, solution of a stochastic pde recorded in seconds, etc. We plan to deal with certain aspects of the following general topics.
Regression Models: This covers logistic regression, categorical regression, time series of counts, and more generally time series following generalized linear models as discussed in Regression Models for Time Series Analysis. Closely related are mixed effects models for longitudinal data.
Financial Time Series: Modeling of volatility by ARCH and GARCH models, prediction of volatility from covariate time series, and finding linear and nonlinear coherence between volatility time series. A recent reference is Nonlinear Time Series Models in Empirical Finance. See also the work of David F. Hendry.
State Space Models: This topic is epitomized by the celebrated "Kalman Filtering and Smoothing" used heavily in navigation and other engineering applications. We shall try to introduce modern semiparametric ideas into state space modeling. See the descriptin of the work by Fokianos et al (2001).
Nonlinear Time Seies: Nonlinear time series can be the result of a nonlinear dynamical system, or the result of a nonlinear system such as Ito-Wiener functional expansion, or the result of a GLM with a non-identity link function, or the result of clipping and thresholding. Examples are discussed in Nonlinear Time Series Analysis, Nonlinear Dynamics, Nonlinear Econometric Modeling in Time Series.
Prerequisites: The minimum requirement for a graduate student is STAT 700 and STAT 650 and some familiarity with statistical regression. Undergraduate students who wish to participate should be familiar with concept discussed in STAT 410 and STAT 420.
Work Plan: The idea of this RIT is active group discussion of the topics described above as well as related topics. Graduate students and faculty are expected to make informal presentations on their research or reading material. Undergraduates are expected to contribute simulation results of time series models.
When/Where/Registration: We meet every Monday at 6:30 PM, in room 1311, Math Building. STAT grad students may register under STAT 689, Section 2001. AMSC grad students may register under AMSC 689, Section 2001.
If you are looking for real time series data, some good sources are: