A Nonparametric Approach to Nonlinear Time Series Analysis: Estimation and Simulation

  • A. Ronald Gallant
  • George Tauchen
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 46)


We describe a method of nonlinear time series analysis suitable for nonlinear, stationary, multivariate processes whose one-step-ahead conditional density depends on a finite number of lags. Such a density can be represented as a Hermite expansion. Certain parameters of the expansion can be set to imply sharp restrictions on the process such as a pure VAR, a pure ARCH, a nonlinear process with homogeneous innovations, etc. The model is fitted using maximum likelihood procedures on a truncated expansion together with a model selection strategy that determines the truncation point. The estimator is consistent for the true density with respect to a strong norm. The norm is strong enough to imply consistency of evaluation functionals and moments of the conditional density. We describe a method of simulating from the density. Simulation can be used for a great variety of applications. In this paper, we give special attention to using simulations to set sup-norm confidence bands. Fortran code is available via ftp anonymous at ccvr1.cc.ncsu.edu ( in directory pub/arg/snp; alternatively, it is available from the authors in the form of a DOS formatted diskette. The code is provided at no charge for research purposes without warranty.


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Copyright information

© Springer-Verlag New York, Inc. 1993

Authors and Affiliations

  • A. Ronald Gallant
    • 1
  • George Tauchen
    • 2
  1. 1.Department of StatisticsNorth Carolina State UniversityRaleighUSA
  2. 2.Department of EconomicsDuke UniversityDurhamUSA

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