Degenerate Multivariate Stationary Processes: Basicity, Past and Future, and Autoregressive Representation.
Abstract
An important problem in prediction theory of weakly stationary stochastic processes (WSSP) is to find conditions on the process, or equivalently on its spectral distribution F, so that the linear least square predictor of a future value of the process admits a mean-convergent series representation in terms of the past (observed) values of the process. Recently, using the notion of positivity of the angle between the past-present and the future subspaces of the process it was shown by Pourahmadi that the series representation of the predictor is possible under some weaker conditions. This was made possible by using the idea of angle due to Helson and Szego for a multivariate extension of this. However these results hold under conditions which require the process to be full rank. The main purpose of this document is to consider the same problem, including their autoregressive representation, for the degenerate WSSP's. Additional keywords: Moving average representation.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1985
- Accession Number
- ADA158879
Entities
People
- A. G. Miamee
- M. Pourahmadi
Organizations
- University of North Carolina at Chapel Hill