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v4.1: Posterior forecasts plots of bvar à la Sims report the median instead of the mean (because the median is less affected by the posterior draws such that the eigenvalues of the companion matrix are outside the unit circle). 

git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@2057 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
adjemian 2008-09-10 15:40:31 +00:00
parent ee67508c0f
commit 4da95da54c
2 changed files with 12 additions and 13 deletions
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4
doc/bvar-a-la-sims.tex
View File

@ -493,11 +493,11 @@ The \texttt{forecast} option is mandatory.
The command will draw \texttt{bvar\_replic} random samples from the posterior distribution. For each draw, it will simulate one path without shocks, and one path with shocks.
\emph{Note:} during the random sampling process, every draw such that the associated companion matrix has eigenvalues outside the unit circle will be discarded. This is meant to avoid explosive time series, especially when using a distant prediction horizon. Since this behaviour induces a distortion of the prior distribution, a message will be displayed if draws are thus discarded, indicating how many have been (knowing that the number of accepted draws is equal to \texttt{bvar\_replic}).
% \emph{Note:} during the random sampling process, every draw such that the associated companion matrix has eigenvalues outside the unit circle will be discarded. This is meant to avoid explosive time series, especially when using a distant prediction horizon. Since this behaviour induces a distortion of the prior distribution, a message will be displayed if draws are thus discarded, indicating how many have been (knowing that the number of accepted draws is equal to \texttt{bvar\_replic}).
The command will produce one graph per observed variable. Each graph displays:
\begin{itemize}
\item a blue line for the mean forecast (equal to the mean of the simulated paths by linearity),
\item a blue line for the posterior median forecast,% (equal to the mean of the simulated paths by linearity),
\item two green lines giving the confidence interval for the forecasts without shocks,
\item two red lines giving the confidence interval for the forecasts with shocks.
\end{itemize}

21
matlab/bvar_forecast.m
View File

@ -36,7 +36,6 @@ function bvar_forecast(nlags)
end
[ny, nx, posterior, prior, forecast_data] = bvar_toolbox(nlags);
sims_no_shock = NaN(options_.forecast, ny, options_.bvar_replic);
sims_with_shocks = NaN(options_.forecast, ny, options_.bvar_replic);
@ -53,7 +52,7 @@ function bvar_forecast(nlags)
% Number of explosive VAR models sampled
p = 0;
% Number of non-explosive VAR models sampled
% Loop counter initialization
d = 0;
while d <= options_.bvar_replic
@ -70,7 +69,6 @@ function bvar_forecast(nlags)
test = (abs(eig(Companion_matrix)));
if any(test>1.0000000000001)
p = p+1;
continue
end
d = d+1;
@ -97,21 +95,22 @@ function bvar_forecast(nlags)
end
if p > 0
disp('')
disp(' ')
disp(['Some of the VAR models sampled from the posterior distribution'])
disp(['were found to be explosive (' int2str(p) ' samples).'])
disp('')
disp(['were found to be explosive (' num2str(p/options_.bvar_replic) ' percent).'])
disp(' ')
end
% Plot graphs
sims_no_shock_mean = mean(sims_no_shock, 3);
sort_idx = round((0.5 + [-options_.conf_sig, options_.conf_sig]/2) * options_.bvar_replic);
sort_idx = round((0.5 + [-options_.conf_sig, options_.conf_sig, 0]/2) * options_.bvar_replic);
sims_no_shock_sort = sort(sims_no_shock, 3);
sims_no_shock_down_conf = sims_no_shock_sort(:, :, sort_idx(1));
sims_no_shock_up_conf = sims_no_shock_sort(:, :, sort_idx(2));
sims_no_shock_median = sims_no_shock_sort(:, :, sort_idx(3));
sims_with_shocks_sort = sort(sims_with_shocks, 3);
sims_with_shocks_down_conf = sims_with_shocks_sort(:, :, sort_idx(1));
sims_with_shocks_up_conf = sims_with_shocks_sort(:, :, sort_idx(2));
@ -119,7 +118,7 @@ function bvar_forecast(nlags)
dynare_graph_init(sprintf('BVAR forecasts (nlags = %d)', nlags), ny, {'b-' 'g-' 'g-' 'r-' 'r-'});
for i = 1:ny
dynare_graph([ sims_no_shock_mean(:, i) ...
dynare_graph([ sims_no_shock_median(:, i) ...
sims_no_shock_up_conf(:, i) sims_no_shock_down_conf(:, i) ...
sims_with_shocks_up_conf(:, i) sims_with_shocks_down_conf(:, i) ], ...
options_.varobs(i, :));
@ -172,7 +171,7 @@ function bvar_forecast(nlags)
sims = squeeze(sims_no_shock(:,i,:));
eval(['oo_.bvar.forecast.no_shock.Mean.' name ' = sims_no_shock_mean(:,i);']);
eval(['oo_.bvar.forecast.no_shock.Median.' name ' = median(sims, 2);']);
eval(['oo_.bvar.forecast.no_shock.Median.' name ' = sims_no_shock_median(:,i);']);
eval(['oo_.bvar.forecast.no_shock.Var.' name ' = var(sims, 0, 2);']);
eval(['oo_.bvar.forecast.no_shock.HPDsup.' name ' = sims_no_shock_up_conf(:,i);']);
eval(['oo_.bvar.forecast.no_shock.HPDinf.' name ' = sims_no_shock_down_conf(:,i);']);