GCov-based portmanteau test

We study nonlinear serial dependence tests based on portmanteau statistics with nonlinear autocovariances for non-Gaussian time series and residuals of dynamic models. A new test with an asymptotic χ2 distribution is introduced for testing nonlinear serial dependence (NLSD) in time series. It stems from the Generalized Covariance (GCov) residual-based specification test with an asymptotic χ2 distribution for semi-parametric dynamic models with i.i.d. non-Gaussian errors. We derive new asymptotic results under local alternative hypotheses on the parameters of a dynamic model, and extend the GCov test to an infinite set of nonlinear autocovariance conditions. A GCov bootstrap test is introduced for size adjustments in finite samples, or residual diagnostics in models estimated parametrically by a maximum likelihood method. The proposed inference method applies to time series exhibiting bubbles, such as commodity prices (e.g., oil, gold) and cryptocurrency rates. A simulation study shows that the tests perform well in applications to mixed causal-noncausal autoregressive models. The GCov specification test is used to assess the fit of a mixed causal-noncausal model of aluminum prices with locally explosive patterns, such as bubbles and spikes, between 2005 and 2024.