Forecasting with generalized bayesian vector auto regressions

Abstract

The effects of using different distributions to parameterize the prior beliefs in a Bayesian analysis of vector autoregressions are studied. The wellknown Minnesota prior of Litterman as well as four less restrictive distributions are considered. TWO of these prior distributions are new to vector autoregressive models. When the forecasting performance of the different parameterizations of the prior beliefs are compared it is found that the prior distributions that allow for dependencies between the equations of the VAR give rise to better forecasts. KEY The use of Vector Autoregressive (VAR) models in applied economics has increased significantly following the criticism of the Cowles Commission approach to the modelling of systems of simultaneous equations (see, for example, Sims, 1980). There has been a shift from the modelling of economic systems with structural equations towards modelling the joint timeseries behaviour of the variables. The frequent use of VARs for modelling the time-series behaviour can partly be explained by their relative ease of use as compared to the richer class of vector ARMA models. The main advantage of VAR models lies in the identification stage, especially if all variables are taken to enter with identical lags. The estimation problem is also particularly simple in the case of identical lags. In the classical analysis, OLS is efficient under the usual assumptions and the Bayesian case is also considerably more straightforward.The main disadvantage of the VAR models is the large number of parameters that need to be estimated. With the sample sizes common in economics the classical estimation procedures often run into degrees-of-freedom problems. In a Bayesian framework, on the other hand, sharp posteriors can often be obtained even with relatively uninformative prior distributions. As a consequence, VAR modelling is one of the areas within applied economics where

Forecasting exchange rates with a large Bayesian VAR

“…Such a prior can be considered as a NormalInverted Wishart version of the traditional Minnesota prior, proposed originally by Doan et al (1984) and Litterman (1986), which has the advantage of avoiding the inconvenient assumption of fixed and diagonal residual variance matrix. The use of this prior for forecasting has been originally proposed by Kadiyala andKarlsson (1993, 1997) In what follows we denote the exchange rate of currency i vis-a-vis the US Dollar at time t as y i,t , and we collect all the exchange rates in the N -dimensional vector Y t = (y 1,t , y 2,t , ..., y N,t ) ′ . Consider the following Vector Autoregression:…”

“…Note that, differently from Kadiyala andKarlsson (1993, 1997), in the above model Y t is regressed directly onto Y t−h , which means that for each forecast horizon , h, a different model is employed. Such an approach, which is known as "direct" forecasting, focuses on minimizing the relevant loss function for each forecast horizon, i.e.…”

Numerical Methods for Estimation and Inference in Bayesian Var-Models

“…In these forecasting applications the combination of prior beliefs and family of prior distributions advocated by Litterman (1980) is often utilized. However, Kadiyala and Karlsson (1993) found that families of prior distributions that allow for dependence between the equations give better forecasts than the essentially univariate`Minnesota prior' of Litterman.…”

“…Two of the more general prior distributions considered by Kadiyala and Karlsson (1993) have the disadvantage that no closed forms exist for the posterior moments of the regression parameters. Consequently, these must be evaluated using numerical methods.…”

Large Vector Autoregressions with Stochastic Volatility and Flexible Priors

“…Step 2: Draw the matrix conditional on the data and , using the conditional (IW) distribution for the posterior given in (23), and derive the matrices A 1 and using the decomposition in equation (19).…”