We consider the problem of implementing simple and efficient Markov chain Monte Carlo (MCMC) estimation algorithms for state space models. A conceptually transparent derivation posterior distribution states is discussed, which also leads to an simulation algorithm that modular, scalable widely applicable. discuss a approach evaluating integrated likelihood, defined as density data given parameters but marginal vector. show this high-dimensional integral can be easily evaluated with minimal...

Summary We develop importance sampling methods for computing two popular Bayesian model comparison criteria, namely, the marginal likelihood and deviance information criterion (DIC) time‐varying parameter vector autoregressions (TVP‐VARs), where both regression coefficients volatilities are drifting over time. The proposed estimators based on integrated likelihood, which substantially more reliable than alternatives. Using US data, we find overwhelming support TVP‐VAR with stochastic...

This article generalizes the popular stochastic volatility in mean model to allow for time-varying parameters conditional mean. The estimation of this extension is nontrival since appears both and variance, its coefficient former time-varying. We develop an efficient Markov chain Monte Carlo algorithm based on band sparse matrix algorithms instead Kalman filter estimate more general variant. methodology illustrated with application that involves U.S., U.K., Germany inflation. results show...

Abstract This paper develops a bivariate model of inflation and survey‐based long‐run forecast that allows for the estimation link between trend forecast. Thus, our possibilities forecasts taken from surveys can be equated with inflation, two are completely unrelated, or anything in between. Using variety measures several countries, we find provide substantial help refining estimates fitting forecasting inflation. It is less helpful to simply equate forecasts.

We introduce a class of large Bayesian vector autoregressions (BVARs) that allows for non-Gaussian, heteroscedastic, and serially dependent innovations. To make estimation computationally tractable, we exploit certain Kronecker structure the likelihood implied by this models. propose unified approach estimating these models using Markov chain Monte Carlo (MCMC) methods. In an application involves 20 macroeconomic variables, find BVARs with more flexible covariance structures outperform...

This article introduces a new model of trend inflation. In contrast to many earlier approaches, which allow for inflation evolve according random walk, ours is bounded ensures that constrained lie in an interval. The bounds this interval can either be fixed or estimated from the data. Our also allows time-varying degree persistence transitory component empirical exercise with CPI inflation, we find work well, yielding more sensible measures and forecasting better than popular alternatives...

We consider an adaptive importance sampling approach to estimating the marginal likelihood, a quantity that is fundamental in Bayesian model comparison and averaging. This motivated by difficulty of obtaining accurate estimate through existing algorithms use Markov chain Monte Carlo (MCMC) draws, where draws are typically costly obtain highly correlated high-dimensional settings. In contrast, we cross-entropy (CE) method, versatile algorithm originally developed for rare-event simulation....

Time varying parameter (TVP) models have enjoyed an increasing popularity in empirical macroeconomics. However, TVP are parameter-rich and risk over-fitting unless the dimension of model is small. Motivated by this worry, article proposes several Varying Dimension (TVD) where can change over time, allowing for to automatically choose a more parsimonious representation, or switch between different representations. Our TVD all fall category dynamic mixture models. We discuss properties these...

We propose importance sampling algorithms based on fast band matrix routines for estimating the observed-data likelihoods a variety of stochastic volatility models. This is motivated by problem computing deviance information criterion (DIC)—a popular Bayesian model comparison that comes in few variants. Although DIC conditional likelihood—obtained conditioning latent variables—is widely used comparing models, recent studies have argued against its use both theoretical and practical grounds....

Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior this setting is the natural conjugate as it facilitates posterior simulation and leads to a range of useful analytical results. This is, however, at expense modeling flexibility, rules out cross‐variable shrinkage, that shrinking coefficients on lags other variables more aggressively than those own lags. We develop has best both worlds: can accommodate while maintaining many results, such...

Many popular specifications for Vector Autoregressions (VARs) with multivariate stochastic volatility are not invariant to the way variables ordered due use of a lower triangular parameterization error covariance matrix. We show that order invariance problem in existing approaches is likely become more serious large VARs. propose specification which avoids this parameterization. presence allows identification proposed model and prove it ordering. develop Markov chain Monte Carlo algorithm...

We compare a number of widely used trend‐cycle decompositions output in formal Bayesian model comparison exercise. This is motivated by the often markedly different results from these decompositions—different have broad implications for relative importance real versus nominal shocks explaining variations output. Using U.S. quarterly GDP, we find that overall best an unobserved components with two features: (i) nonzero correlation between trend and cycle innovations (ii) break growth 2007....

In this paper, we develop a bivariate unobserved components model for inflation and unemployment. The are trend the non-accelerating rate of unemployment (NAIRU). Our also incorporates time-varying Phillips curve persistence. What sets paper apart from existing literature is that do not use unbounded random walks components, but rather bounded walks. For instance, NAIRU assumed to evolve within bounds. empirical work shows importance bounding. We find our forecasts better than many...