Testing for the Absence of Score-Driven Parameter Dynamics

This paper proposes a quasi-likelihood ratio (QLR) test for the null of constant parameters against the alternative of score-driven parameter dynamics. Score-driven models have been widely used in the literature to capture time variation in parameters across a diverse range of both continuous and discrete, univariate and multivariate time series models, with or without random regressors. A formal testing procedure, however, is lacking thus far. Our QLR test addresses two key challenges: (i) parameters may lie on the boundary of the parameter space, and (ii) nuisance parameters are not identified under the null. The test statistic’s non-standard asymptotic distribution takes a simple form that only depends on the specified parameter space and is invariant to the specific formulation of the score-driven model and its degree of nonlinearity. Consequently, the asymptotic distribution applies to a wide range of score-driven models and can easily be simulated to conduct inference. We illustrate the new test using several models from the score-driven literature and show that the limiting distribution provides an adequate approximation for inference in finite samples.