The function $F$ has an analytical form, which is given by the normalization constants of matrix-normal and inverse-Wishart densities\footnote{Function \texttt{matricint} of file \texttt{bvar\_density.m} implements the calculation of the log of $F$.}:

The function $F$ has an analytical form, which is given by the normalization constants of matrix-normal and inverse-Wishart densities:\footnote{Function \texttt{matricint} of file \texttt{bvar\_density.m} implements the calculation of the log of $F$.}

Please also note that if option \texttt{loglinear} had been specified in a previous \texttt{estimation} statement, without option \texttt{logdata}, then the BVAR model will be estimated on the log of the provided dataset, for maintaining coherence with the DSGE estimation procedure.

\emph{Restrictions related to the initialization of lags:} in DSGE estimation routines, the likelihood (and therefore the marginal density) are evaluated starting from the observation numbered \texttt{first\_obs + presample} in the datafile\footnote{\texttt{first\_obs} points to the first observation to be used in the datafile (defaults to 1), and \texttt{presample} indicates how many observations after \texttt{first\_obs} will be used to initialize the Kalman filter (defaults to 0).}. The BVAR estimation routines use the same convention (i.e. the first observation of $Y^+$ will be \texttt{first\_obs + presample}). Since we need $p$ observations to initialize the lags, and since we may also use a training sample, the user must ensure that the following condition holds (estimation will fail otherwise):

\emph{Restrictions related to the initialization of lags:} in DSGE estimation routines, the likelihood (and therefore the marginal density) are evaluated starting from the observation numbered \texttt{first\_obs + presample} in the datafile.\footnote{\texttt{first\_obs} points to the first observation to be used in the datafile (defaults to 1), and \texttt{presample} indicates how many observations after \texttt{first\_obs} will be used to initialize the Kalman filter (defaults to 0).} The BVAR estimation routines use the same convention (i.e. the first observation of $Y^+$ will be \texttt{first\_obs + presample}). Since we need $p$ observations to initialize the lags, and since we may also use a training sample, the user must ensure that the following condition holds (estimation will fail otherwise):

@@ -592,16 +613,5 @@ Schorfheide, Frank (2004), ``\textit{Notes on Model Evaluation}'', Department of

Sims, Christopher (2003), ``\textit{Matlab Procedures to Compute Marginal Data Densities for VARs with Minnesota and Training Sample Priors}'', Department of Economics, Princeton University

\section*{Acknowledgements}

Many thanks to Christopher Sims for his BVAR Matlab routines, and to St\'ephane Adjemian and Michel Juillard for their helpful support.

\section*{License}

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.