Testing linearity for stationary time series using the sample interquartile range (Q2740047)

The author proposes a test for the hypothesis \(H_0\) of linearity of a stationary time-series. The test is based on the values of normalized empirical bispectrum (obtained by smoothing the second- and third-order periodograms). Squared values of the bispectrum are evaluated at a discrete set of frequencies in the principal domain. For the set of these values a sample interquartile range is computed. This quantity is used as a test statistics.NEWLINENEWLINENEWLINEThe author evaluates the asymptotic significance level of the test using the fact that under the null hypothesis the theoretical normalized bispectrum is a constant and normalized empirical bispectrum values are asymptotically normal and independent. Computational and simulation results are presented.