Journal of Time Series Analysis

A New Test of Linearity of Time Series Based on the Bispectrum

Journal Article

The linearity of a time series is tested by use of the bispectrum. We define the time series to be linear if the best predictor is linear. The bispectrum is estimated by stretching the data and smoothing by the Subba Rao–Gabr optimal window. The null hypothesis tested here is that the best predictor is linear against the alternative that the best predictor is quadratic. It turns out that the test statistic is asymptotically χ2‐distributed under the hypothesis that the time series is linear. The results are demonstrated using simulated and real data.

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