BVAR Steady-State prior

The Bayesian Vector Autoregressive (BVAR) model is a Bayesian version of the Vector Autoregressive (VAR) model with the Villani Steady-State prior.

Bayesian inference

Classical statistical models adhere to a frequentist approach, where the assumption is that there exists an underlying true model. If the model is estimated on multiple random samples, the estimate of the model from data will be closer than a constant αα to the true model for a certain proportion of the samples.

Bayesian statistics begin with a prior which describes a certain prior belief of the underlying process generating the data. After the data is observed, the prior belief and the data are combined through Bayes' theorem, and a posterior distribution which describes the probability of getting different values given both the prior beliefs and the data.

Villani Steady-State prior

The steady-state prior assumes a prior belief of each variable eventually returning to a steady state. This is regarded compatible with economic theory as economists usually believe that most macroeconomic variables will return to some predetermined steady state after a shock to the system.

How does Indicio fit a BVAR model?

The first step is to select steady state priors for each variable. For example, if the model includes inflation and we believe that it will eventually reach a steady state of 2%, we can set the prior belief of the steady state to be 0.02. This must be done for each variable in the model before it can be built.

The model is then fitted to the data by drawing samples in a Markov Chain Monte Carlo (MCMC) sampling algorithm. These samples are drawn proportional to how probable they are given the data and the prior. This way, a large sample of parameter sets is obtained, representing the density of the parameter space. These samples are then used to produce a sample of forecasts, which represent the density of the forecast given the priors, data and the model.

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