Tucker McElroy, U.S. Census Bureau
Project Description/Abstract
We develop a theory of polyspectral factorization, providing new mathematical results for polyspectral densities. New bijections between a restricted space of higher-dimensional cepstral coefficients (where the restrictions are induced by the symmetries of the polyspectra) and the autocumulants are derived. Secondly, the theoretical background for a new quadratic prediction method for time series is developed through three main contributions: (1) a new theory for infinite arrays and their factorization is developed, generalizing multivariate spectral factorization theory; (2) the formula for the quadratic h-step ahead forecast filter (based on an infinite past) is derived; (3) a necessary and sufficient condition involving the bispectrum is derived, for discerning when quadratic prediction offers a benefit over linear prediction.
Co-Authors
Dhrubajyoti Ghosh, Washington University, St. Louis
Soumendra Lahiri, Washington University, St. Louis