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The Identification of a Particular Nonlinear Time Series System

David R. Brillinger
Biometrika
Vol. 64, No. 3 (Dec., 1977), pp. 509-515
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2345326
Stable URL: http://www.jstor.org/stable/2345326
Page Count: 7
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The Identification of a Particular Nonlinear Time Series System
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Abstract

A nonlinear time series system is considered. The system has the property that the output series corresponding to a given input series is the sum of a noise series and the result of applying in turn the operations of linear filtering, instantaneous functional composition and linear filtering to the input series. Given a stretch of Gaussian input series and corresponding output series, estimates are constructed of the transfer functions of the linear filters, up to constant multipliers. The investigation discloses that for such a system, the best linear predictor of the output given Gaussian input, has a broader interpretation than might be suspected. The result is derived from a simple expression for the covariance function of a normal variate with a function of a jointly normal variate.

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