Degenerate Multivariate Stationary Processes: Basicity, Past and Future, and Autoregressive Representation.
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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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 WSSPs. Additional keywords Moving average representation.
- Statistics and Probability