Patrick Crutcher

My Research Interests

In general, I am interested in time series analysis with applications in environmental sciences, clinical trials, and finance. In particular, I am focusing my research on applications of singular spectrum analysis (SSA). SSA decomposes an observed time series into principal components. This decomposition utilizes the Singular Value Decomposition(SVD) of a lagged covariance(trajectory) matrix of observed values. The approach is very similar to Principal Components Analysis. SSA processing is a decomposition of the time series into several components, which can often be identified as trends, seasonalities and other oscillatory series, or noise components. SSA is good at isolating oscillatory behavior via paired eigenelements.

It can be essentially broken down into 2 main stages: Decomposition and Reconstruction. We are actively interested in optimal ways of reconstruction using various clustering algorithms on prinicpal components.



Decomposition

1. Embedding time series into a trajectory matrix

2. SVD of the trajectory matrix



Reconstruction

3. PCA and selection of the dominant features by grouping the SVD components

4. Reconstruction of original time series using selected components



This work is being doing done under the supervision of Professor Jan De Leeuw. You can find our package for implementing SSA on R-Forge.