Statistics and Data Science Seminar: "On the Construction, Simulation, and Fitting of Second Order Forecastable Processes"

Speaker: Tucker McElroy, U.S. Census Bureau

Abstract: Although the existence of a stationary nonlinear process with given autocumulant functions is guaranteed by Nisio (1960), it is unclear how to choose the corresponding polynomial filters of the process inputs accordingly. We show how to recursively construct a second order forecastable process -- defined by the property that its optimal one-step ahead forecast polynomial filter is quadratic and irreducible -- from given polyspectra of order 2, 3, and 4, via using the quadratic forecast filter.  We characterize reducibility of the quadratic filter in terms of Granger non-causality of product pairs of past values, and apply the recursive algorithm to the simulation and fitting of nonlinear time series. Examples with an order 2 polynomial process and a bilinear process are provided.

Hosts: Likai Chen and Debashis Mondal

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