Instructor: Richard Davis (Columbia University)
AUGUST 18, 1:30—5 PM
ROOM: LInC 368
In this course, we will take another look at modeling time series that exhibit certain types of nonstationarity. Often one encounters time series for which segments look stationary, but the whole ensemble is nonstationary. On top of this, each segment of the data may be further contaminated by an unknown number of innovational and/or additive outliers; a situation that presents interesting modeling challenges. We will seek to find the best fitting model in terms of the minimum description length principle. As this procedure is computationally intense, strategies for accelerating the computations are required. Numerical results from simulation experiments and real data analyses, some of which come from Google trends, show that our proposed procedure enjoys excellent empirical properties. In the case of no outliers, there is an underlying theory that establishes consistency of our method. The theory is based on an interesting application of the functional law of the iterated logarithm.
Course Outline
- Motivation/examples
- Introduction to the base model
- Model selection using Minimum Description Length (MDL)
- Optimization of objective function
- Applications
- Hands-on use of AutoPARM
- Some theory (consistency and nonconsistency)
- AutoPARM w/ outliers
- Applications to Google trends data