Real-time performance & updated variables

Dynare help (legacy posts)
1

Dear all,

Consider an unobserved-components model that decomposes a series into cycles and trends. One would like to see its real-time performance compared to the smoothed estimate. The t|t projection can be found in oo_.UpdatedVariables structure, and called by the smoother' option in estimation. However, I would like to see also the updates in between those two extremes, e.g. how fast the real-time estimate converges to the smoothed one. For that purpose, I'd like to see theupdated’ variables after a quarter, year, and so on. It looks like there is no such a built-in feature in Dynare 4.4.3 yet. What would be the easiest way to implement such? I guess, the output should be generated on-demand only, so there should be some option similar to, and ideally, incorporated into filter_step_ahead (but with negative entries).

2

Dear Ginters,
which information sets exactly are you after? What do you mean with

?

3
  1. For quarterly data, these would be smoothed endogenous variables at t|t+1, t|t+4, t|t+12, t|t+20 that is, to see not only t|t but also how smoothed variables (e.g. the output gap) evolve when new information comes. This info should be readily available from the smoother.
  2. I referred to filter_step_ahead because it produces t|t-k, k>0; thus if k<0 it would give the above without introducing a new option in the estimation command.

Alternatively, I could estimate the model by iteratively increasing the sample size but that is a bit more cumbersome/time consuming.

4

Are we talking about fixed parameters? Or are parameters updated as well with the information set?

5

Fixed parameters.

6

In that case, I think looping over the calibrated smoother is the only way to go and it should be relatively quick. The reason is that than information set t|t+k is created in the Kalman smoother via a backward pass where you have to start at the end of the sample.

7

Thanks.
For those interested, below is the code snippet of my interpretation of `looping over a calibrated smoother’ in a single mod-file using @#for-loop.

[code]
%
% Observed variables
%

varobs ym1, ym2, ym3; % GDP, Credit and Prices series

%----------------------------------------------------------------
% 5. Bayesian estimation
%----------------------------------------------------------------

verbatim;
% define real-time matrices
% variable 1
trend1=nan(100,100);
slope1=nan(100,100);
cycle1=nan(100,100);
% variable 2
trend2=nan(100,100);
slope2=nan(100,100);
cycle2=nan(100,100);
% variable 3
trend3=nan(100,100);
slope3=nan(100,100);
cycle3=nan(100,100);
end;

options_.console_mode=1; %(default: 0)
@#for mysample in 21:85
estimation (
nobs=@{mysample}], % 21:85
datafile = lv_3data_hhloans,
nodisplay,
nograph,
graph_format = pdf,
nodiagnostic,
diffuse_filter,
kalman_algo = 0,
mh_replic = 0,
mh_nblocks = 1,
filtered_vars,
smoother,
mode_file=multiv_uoc_lv_hhloans6_mode,
mode_compute = 0,
plot_priors = 0,
forecast = 0
) mmu1 mmu2 mmu3 car1 car2 car3;

%----------------------------------------------------------------
% 6. Reporting
%----------------------------------------------------------------
%
% use this for verbatim mode
mynobs=@{mysample};
verbatim;

for i = 1:3
%if laplace only
% get the smoothed trend and cycle
%eval( ‘ym_ = ym’ num2str(i) ‘;’ ]);
eval( ‘trend_ = oo_.SmoothedVariables.mmu’ num2str(i) ‘;’ ]);
eval( ‘cycle_ = oo_.SmoothedVariables.car’ num2str(i) ‘;’ ]);
% eval( ‘irreg_ = oo_.SmoothedShocks.e_irr’ num2str(i) ‘;’ ]);

% form a matrix of real time estimates
eval( 'trend' num2str(i) '(1:mynobs,mynobs-20)= trend_;']);
eval( 'slope' num2str(i) '(2:mynobs,mynobs-20)= diff(trend_);' ]);
eval( 'cycle' num2str(i) '(1:mynobs,mynobs-20)= cycle_;' ]);

end;

end;

@#endfor

% plot all real-time cycles for variable 1 (GDP)
figure(1)
plot(cycle1)

% extract only t|t, t|t+4, t|t+12 and t|t+20
verbatim;
% t|t estimate
mystep=0;
cycle1_t_t=nan(100,1);
for ii=21:85-mystep
cycle1_t_t(ii)=cycle1(ii,ii-20+mystep);
end

% t|t+4 estimate
mystep=4;
cycle1_t_tp4=nan(100,1);
for ii=21:85-mystep
cycle1_t_tp4(ii)=cycle1(ii,ii-20+mystep);
end

% t|t+12 estimate
mystep=12;
cycle1_t_tp12=nan(100,1);
for ii=21:85-mystep
cycle1_t_tp12(ii)=cycle1(ii,ii-20+mystep);
end

% t|t+20 estimate
mystep=20;
cycle1_t_tp20=nan(100,1);
for ii=21:85-mystep
cycle1_t_tp20(ii)=cycle1(ii,ii-20+mystep);
end

figure(2)
plot(cycle1_t_t,’:black’)
hold on;
plot(cycle1_t_tp4,’-.black’)
plot(cycle1_t_tp12,’–red’)
plot(cycle1_t_tp20,‘red’)
hold off;
legend(‘t|t’,‘t|t+4’,‘t|t+12’,‘t|t+20’)

end;[/code]

64 iterations plus plots go in 16sec.

8

That works, but I was rather thinking about looping over the

command. See github.com/DynareTeam/dynare/blob/master/tests/fs2000/fs2000_calib.mod