A note on Portmanteau tests for conditional heteroscedastistic models

We derive the asymptotic distribution of autocorrelation of squared residuals for a wide class of conditional heteroscedastistic models when some parameters lie on the boundary. The limiting distribution of the portmanteau test statistic is no longer chi-square but taking a quadratic form of a normally distributed random variable which is projected onto a convex cone. Simulations are conducted and they reveal that using conventional chi-square asymptotics may lead to erroneous decisions due to size distortion when boundary parameters are present. •A portmanteau test is proposed for APARCH-X models.•The limiting distribution of the test is no longer χ2 when boundary parameters exist.•Over-parametrization may lead to erroneous decision if incorrect χ2 asymptotics is used.