Specification tests for time-varying parameter models with stochastic volatility

We propose an easy technique to test for time-variation in coefficients and volatilities. Specifically, by using a noncentered parameterization for state space models, we develop a method to directly calculate the relevant Bayes factor using the Savage-Dickey density ratio — thus avoiding the computation of the marginal likelihood altogether. The proposed methodology is illustrated via two empirical applications. In the first application we test for time-variation in the volatility of inflation in the G7 countries. The second application investigates if there is substantial time-variation in the NAIRU in the US