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Keywords:

  • Heteroscedastic;
  • intercorrelated time series;
  • linearity testing;
  • nonlinear;
  • nonparametric estimation;
  • panel

Abstract.  We consider nonparametric estimation and testing of linearity in a panel of intercorrelated time series. We place the emphasis on the situation where there are many time series in the panel but few observations for each of the series. The intercorrelation is described by a latent process, and a conditioning argument involving this process plays an important role in deriving the asymptotic theory. To be accurate the asymptotic distribution of the test functional of linearity requires a very large number of observations, and bootstrapping gives much better finite sample results. A number of simulation experiments and an illustration on a real data set are included.