Asymmetric Conjugate Priors for Large Bayesian VARs

Abstract

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.

Application of Bayesian Regression Model in Financial Stock Market Forecasting

“…Stock market factors have random sampling attributes from the underlying variable population, with a real magnitude that is randomly distributed [9]. Inference rules incorporate universal constraints based on unbiased estimators, hypothesis testing, and confidence intervals, relying on large-sample approximations [5]. However, it is infrequent for financial data to adhere to these assumptions.…”

“…It is crucial to bear in mind that many of these strong assumptions are completely irrelevant in a Bayesian context. In Bayesian statistics, the dataset is considered fixed, and the parameters are considered uncertain [5]. Hence, probability distributions can be altered when new information becomes available under the Bayesian framework.…”

“…There is an essential link between inference, computing, and models with practical applicability. By comparison, the significant advancements in posterior simulators in the past two decades have a notable impact on developing new models [5]. Since these models' applicability depends on available computational tools, powerful processors facilitate the making of influential previous assumptions, which are successful in compensating for a wasteful parameterization.…”

“…The market structure shifts over time, and occasionally, structural change happens suddenly. To successfully manage and reconcile the concept of probability, it is imperative to use dynamic Bayesian modeling processes [5]. These methods control the process of updating expectations while incorporating new information with careful respect to fundamental laws of probability [1].…”

“…Scholars utilize these prior distributions differently, either via the Conjugate or the Noninformative prior. The Conjugate prior is when the posterior distribution and the initial distribution have the same form, while the Noninformative is when they differ [5]. The Noninformative Prior distribution is utilized when scholars have limited previous knowledge or information.…”