A Computationally Efficient Mixture Innovation Model for Time-Varying Parameter Regressions

The mixture innovation (MI) model places spike-and-slab mixture distributions on the innovations of time-varying regression coefficients and allows for a wide variety of time variation patterns. Despite its appeal, estimating the MI model can be computationally prohibitive when the number of regressors is large. For practical applications, this paper proposes a specification of the MI model in which the 0/1 mixture indicator in the original MI model is approximated by a logistic function of latent continuous random-walk variables. Through Metropolis-Hastings steps, the latent variables and hence the approximated mixture indicators can be sampled much more efficiently than directly sampling the 0/1 mixture indicators in the original MI model. An efficient MCMC algorithm is developed to estimate the new model and is free of manual tuning. I show in a simulation study 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 with a relatively large number of regressors for which the original MI model is practically infeasible