Nonparametric Functional Estimation and Related Topics pp 541-552

Part of the NATO ASI Series book series (ASIC, volume 335) | Cite as

Nonparametric Estimation of a Class of Nonlinear Time Series Models

  • M. Pawlak
  • W. Greblicki

Abstract

The problem of estimation of nonlinear time series models which are a composition of nonlinear elements and linear stochastic processes is considered. The compositions studied include the cascade and parallel connections. The problem of nonparametric estimation of underlying nonlinearities is examined. It is resolved by solving Fredholm’s integral equations of the second kind arising in the estimation problem. As a result, the nonparametric orthogonal series estimates of nonlinearities are derived and their asymptotic as well as some small sample properties are established.

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Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • M. Pawlak
    • 1
  • W. Greblicki
    • 2
  1. 1.Department of Electrical and Computer EngineeringUniversity of ManitobaWinnipegCanada
  2. 2.Institute of Engineering CyberneticsTechnical University of WroclawPoland

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