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Keywords:

  • Frequency domain generalized empirical likelihood;
  • spectral restrictions;
  • stationary process

This paper is concerned with a version of empirical likelihood method for spectral restrictions, which handles stationary time series data via the frequency domain approach. The asymptotic properties of frequency domain generalized empirical likelihood are studied for either strictly stationary processes with vanishing cumulant spectral density function of order 4 or linear processes generated by iid innovations with possibly non-zero fourth order cumulant. Several statistics for testing parametric restrictions, over-identified spectral restrictions, and additional spectral restrictions are shown to have the limiting chi-squared distributions. Some numerical results are presented to investigate the finite sample performance of the proposed procedures. Copyright © 2013 John Wiley & Sons, Ltd.