Speaker: 
Dr. Peter Sherman
ISU Department of Aerospace Engineering and Department of Statistics

The Exact Covariance Eigenstructure for AR(1) Processes

We offer a detailed description of the complete eigenstructure of the covariance matrix, R, associated with a sampled Gauss-Markov process (also commonly referred to as first order autoregressive or AR(1) process). This description is exact for any matrix size T. Having this allows us to show that the eigenvectors of R do not converge to pure cosines as T goes to infinity. It also allows us to carry out a detailed investigation of how the eigenstructure of a common circulant-based approximation of R compare to that of R, itself. Finally, we demonstrate the practical value of our results in relation to the classic signal-plus-noise problem.

Refreshments at 3:45pm in Snedecor 2101.