A computationally efficient mixture innovation model for time-varying parameter regressions

Abstract

The mixture innovation (MI) model places a spike-and-slab mixture distribution for the innovations of time-varying regression coefficients and permits flexible time variation patterns while allowing for dynamic shrinkage. Despite its appeal, the standard Bayesian algorithm to block sample the vector of 0/1 mixture indicators at each time $t$ needs to evaluate the model likelihood over all its $2^K$ scenarios for a regression model with $K$ regressors and becomes impractical when $K$ grows. As an alternative, a new specification of the MI model is proposed in which the 0/1 mixture indicators in the original MI model are approximated by a logistic function of latent continuous variables. As such the model likelihood only needs to be evaluated twice in an Metropolis-Hastings step to block update the latent variables and hence the approximated mixture indicators at each time $t$, offering large improvement in computational efficiency while keeping the benefits of the MI model. An efficient MCMC algorithm is developed to estimate the new model. A simulation study shows that the new model can achieve the same level of estimation accuracy as the original MI model but at a much smaller computation cost. The new model is further tested in two empirical applications where block sampling the mixture indicators at each time $t$ in the original MI model is practically infeasible.