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Identification of Nonlinear Time Series from First Order Cumulative Characteristics

Ian W. McKeague and Mei-Jie Zhang
The Annals of Statistics
Vol. 22, No. 1 (Mar., 1994), pp. 495-514
Stable URL: http://www.jstor.org/stable/2242466
Page Count: 20
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Identification of Nonlinear Time Series from First Order Cumulative Characteristics
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Abstract

A new approach to the problem of identifying a nonlinear time series model is considered. We argue that cumulative lagged conditional mean and variance functions are the appropriate "signatures" of a nonlinear time series for the purpose of model identification, being analogous to cumulative distribution functions or cumulative hazard functions in iid models. We introduce estimators of the cumulative lagged conditional mean and variance functions and study their asymptotic properties. A goodness-of-fit test for parametric time series models is also developed.

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