Alexandria

a software for Bayesian time-series econometrics applications

Alexandria is a Matlab package for Bayesian time-series econometrics applications. This is version 3.0, which includes Bayesian regression, Bayesian vector autoregression, Bayesian VEC/VARMA models, and Bayesian nowcasting.

Alexandria offers a range of Bayesian linear regression models:

• maximum likelihood / OLS regression (non-Bayesian)
• simple Bayesian regression
• hierarchical (natural conjugate) Bayesian regression
• independent Bayesian regression with Gibbs sampling
• heteroscedastic Bayesian regression
• autocorrelated Bayesian regression

Alexandria also offers a large number of Bayesian vector autoregression models and applications:

• maximum likelihood (OLS) VAR
• Litterman Minnesota prior
• normal-Wishart prior
• independent prior with Gibbs sampling
• dummy observation prior
• large Bayeisian VAR prior
• Bayesian oxy-SVAR

prior customization:

• constrained coefficients
• dummy extensions (sums-of-coefficients, initial observation,long-run prior)
• stationary priors
• hyperparameter optimization from marginal likelihood

structural identification:

• Cholesky
• triangular factorization
• restrictions: sign and zero restrictions on IRFs, narrative on shocks and historical decomposition

applications:

• forecasts
• impulse response function
• forecast error variance decomposition
• historical decomposition
• conditional forecasts (agnostic and sctructural approaches, allowing for hard and soft conditions)

Alexandria also includes Bayesian VEC and VARMA models, along with many applications:

• Bayesian VEC: uninformative, horseshoe and selection priors; general and reduced-rank approaches
• Bayesian VARMA: Minnesota prior on autoegressive and lag coefficients; residuals estimated from Bayesian state-space modelling
• structural identification and applications are the same as the Bayesian VAR models

The current version introduces Bayesian nowcasting models, along with many applications:

• Mixed Frequency Bayesian VAR: allows for mixed frequency, missing observations, and frequency decomposition; all BVAR applications are available with the MF-BVAR.
• Bayesian Dynamic Factor Model: extract structural factors from high and low frequency features; nowcasts in real time; also permits structural IRFs, variance and historical decomposition.
• Bayesian MIDA regression: 3 priors (Minnesota, Horseshoe, Bayesian lasso) and 3 representations (unrestricted MIDAS, Almon, Fourier).

Alexandria is user-friendly and can be used from a simple Graphical User Inteface (GUI). More experienced users can also run the models directly from the command line by using the model classes and methods.