Prediction Theory of Periodically Correlated Stochastic Processes
Final rept. 9 Feb 2011-15 Aug 2014
HAMPTON UNIV VA
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The research dealt with the prediction problem for periodically correlated sequences, that is the stochastic sequences whose mean and covariance structure vary with time in a periodic way. We aimed at sequences with large periods. It has been known already for years that in order to do a reliable forecasting of periodically correlated sequences with large period or continuous time processes the standard method of rephrasing the problems in terms of multivariate stationary sequences does not work because of a huge number of unknown parameters. Our main effort was to develop an alternative technique for analysis such sequences . In the first published paper we proposed a new method based on a notion of a square factor of the spectrum of the process. In subsequent two papers we showed that this technique is very efficient. We successfully used it to study structure, regularity, autoregressive representation, innovation, and other questions related to prediction of periodically correlated sequences.
- Statistics and Probability