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 nonaccelerating inflation rate of unemployment (NAIRU) in the United States.