Misspecification tests based on quantile residuals

We develop quantile residual‐based misspecification tests and apply them to non‐linear time series models for which conventional residuals are unsuited. We formulate a general framework and use it to obtain computationally simple tests aimed at detecting autocorrelation, conditional heteroscedasticity and non‐normality in quantile residuals. These tests are generalizations of similar previous tests based on conventional residuals and the Lagrange Multiplier principle. According to simulations on mixture models our tests are reasonable in size and more powerful than alternatives in the literature. An empirical example on interest rate data illustrates the usefulness of these methods.