Simultaneous Diagnostic Testing for Linear-Nonlinear Dependence in Time Series
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Several goodness-of-fit tests have been proposed to detect linearity in stationary time series based on the autocorrelations of the residuals. Others have been developed based on the autocorrelations of the square residuals or based on the cross-correlations between residuals and their squares to test for nonlinearity. In this paper, we propose omnibus portmanteau tests that can be used for detecting, simultaneously, many linear, bilinear, and nonlinear dependence structures in stationary time series based on combining all these correlations. An extensive simulation study is conducted to examine the finite sample performance of the proposed tests. The simulation results show that the proposed tests successfully control the Type I error probability and tend to be more powerful than other tests in most cases. The efficacy of the proposed tests is demonstrated through the analysis of Amazon.com, Inc., daily log-returns.
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