##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability \& Statistics Seminar

## Tucker McElroy

#### US Census Bureau

## Polyspectral Factorization

##### Abstract:

This presentation contributes to the theoretical background for a new quadratic prediction method for time series. 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 auto-cumulants are derived. Applications to modeling are developed; in particular, it is shown that semi-parametric nonlinear time series modeling can be accomplished by approximation of the cepstral representation of polyspectra.

Host: Wenxin Zhou

### March 17, 2021

### 3:00 PM

### Location: https://ucsd.zoom.us/j/92649390991

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