Stochastic Model Specification Search for Time-Varying Parameter VARs

Self Cite

We develop importance sampling methods for computing two popular Bayesian model comparison criteria, namely, the marginal likelihood and deviance information criterion (DIC) for TVP-VARs with stochastic volatility. The proposed estimators are based on the integrated likelihood, which are substantially more reliable than alternatives. Specifically, integrated likelihood evaluation is achieved by integrating out the time-varying parameters analytically, while the log-volatilities are integrated out numerically via importance sampling. Using US and Australian data, we find overwhelming support for the TVPVAR with stochastic volatility compared to a conventional constant coefficients VAR with homoscedastic innovations. Most of the gains, however, appear to have come from allowing for stochastic volatility rather than time variation in the VAR coefficients or contemporaneous relationships. Indeed, according to both criteria, a constant coefficients VAR with stochastic volatility receives similar support as the more general model with time-varying parameters.

Section: Tvp-vars With Stochastic Volatilitymentioning

confidence: 99%

Bayesian Model Comparison for Time-Varying Parameter VARs with Stochastic Volatility

Chan

Eisenstat

2015

Self Cite

“…There is now a large empirical literature that shows that models with stochastic volatility tend to forecast substantially better (Clark, 2011;D'Agostino, Gambetti, and Giannone, 2013;Cross and Poon, 2016). In future work, it would be useful to develop similar efficient posterior samplers for large BVARs with stochastic volatility, such as the models in Eisenstat, Chan, and Strachan (2018) and Carriero, Clark, and Marcellino (2019). In addition, it would be interesting to use Proposition 1 to work out a way to construct a multivariate stochastic volatility model that is invariant to reordering of the variables.…”

Section: Concluding Remarks and Future Researchmentioning

confidence: 99%

Asymmetric Conjugate Priors for Large Bayesian VARs

Chan

2019

Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior in this setting is the natural conjugate prior as it facilitates posterior simulation and leads to a range of useful analytical results. This is, however, at the expense of modelling exibility, as it rules out cross-variable shrinkage-i.e. shrinking coefficients on lags of other variables more aggressively than those on own lags. We develop a prior that has the best of both worlds: it can accommodate cross-variable shrinkage, while maintaining many useful analytical results, such as a closed-form expression of the marginal likelihood. This new prior also leads to fast posterior simulation-for a BVAR with 100 variables and 4 lags, obtaining 10,000 posterior draws takes less than half a minute on a standard desktop. In a forecasting exercise, we show that a data-driven asymmetric prior outperforms two useful benchmarks: a data-driven symmetric prior and a subjective asymmetric prior.

“…For example, Koop and Korobilis (2013) propose an approximation to the posterior distribution by using forgetting factors to reduce the computational burden related to repeated Kalman filter runs. Eisenstat, Chan, and Strachan (2016) propose stochastic model specification search for TVP-VARs with stochastic volatility in order to deal with overfitting and the typically imprecise inference in these highly parameterised models (see also Frühwirth-Schnatter and Wagner, 2010;Belmonte, Koop, and Korobilis, 2014). de Wind and Gambetti (2014) introduce cross-equation restrictions on the time variation.…”

Section: Introductionmentioning

confidence: 99%

Forecasting with Bayesian Vector Autoregressions with Time Variation in the Mean

Bańbura

Vlodrop

2018

We develop a vector autoregressive model with time variation in the mean and the variance. The unobserved time-varying mean is assumed to follow a random walk and we also link it to long-term Consensus forecasts, similar in spirit to so called democratic priors. The changes in variance are modelled via stochastic volatility. The proposed Gibbs sampler allows the researcher to use a large cross-sectional dimension in a feasible amount of computational time. The slowly changing mean can account for a number of secular developments such as changing inflation expectations, slowing productivity growth or demographics. We show the good forecasting performance of the model relative to popular alternatives, including standard Bayesian VARs with Minnesota priors, VARs with democratic priors and standard time-varying parameter VARs for the euro area, the United States and Japan. In particular, incorporating survey forecast information helps to reduce the uncertainty about the unconditional mean and along with the time variation improves the long-run forecasting performance of the VAR models.