Summary
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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Brillinger, D.R. (2012). The identification of a particular nonlinear time series system. In: Guttorp, P., Brillinger, D. (eds) Selected Works of David Brillinger. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1344-8_35
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DOI: https://doi.org/10.1007/978-1-4614-1344-8_35
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