136 lines
4.0 KiB
Matlab
136 lines
4.0 KiB
Matlab
function [ya, yass, gya, gyass] = quarterly2annual(y,yss,GYTREND0,type,islog,aux)
|
|
% function [ya, yass, gya, gyass] = quarterly2annual(y,yss,GYTREND0,type,islog,aux)
|
|
% transforms quarterly (log-)level time series to annual level and growth rate
|
|
% it accounts for stock/flow/deflator series.
|
|
%
|
|
% INPUTS
|
|
% y quarterly time series
|
|
% yss steady state of y
|
|
% GYTREND0 growth rate of y
|
|
% type 1 sum (default)
|
|
% 2 average
|
|
% 3 last period (Q4)
|
|
% 4 geometric average
|
|
% 5 annual price as quantity weighted average
|
|
% 6 annual quantity from average price
|
|
% 7 annual nominal from Q real and deflator
|
|
% islog 0 level (default)
|
|
% 1 log-level
|
|
% 2 growth rate Q frequency
|
|
% aux optional input used when type>4
|
|
%
|
|
%
|
|
% OUTPUTS
|
|
% ya annual (log-)level
|
|
% yass annual steadystate (log-)level
|
|
% gya annual growth rate
|
|
% gyass annual growth rate steadystate
|
|
|
|
% Copyright (C) 2017 Dynare Team
|
|
%
|
|
% This file is part of Dynare.
|
|
%
|
|
% Dynare is free software: you can redistribute it and/or modify
|
|
% it under the terms of the GNU General Public License as published by
|
|
% the Free Software Foundation, either version 3 of the License, or
|
|
% (at your option) any later version.
|
|
%
|
|
% Dynare is distributed in the hope that it will be useful,
|
|
% but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
% GNU General Public License for more details.
|
|
%
|
|
% You should have received a copy of the GNU General Public License
|
|
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
|
|
|
|
if nargin ==0
|
|
disp('[ya, yass, gya, gyass] = quarterly2annual(y,yss,GYTREND0,type,islog);')
|
|
return
|
|
end
|
|
|
|
if nargin<4 || isempty(type)
|
|
type=1;
|
|
end
|
|
if nargin<5 || isempty(islog)
|
|
islog=0;
|
|
end
|
|
if isstruct(aux)
|
|
yaux=aux.y;
|
|
yauxss=aux.yss;
|
|
islogaux=aux.islog;
|
|
GYTREND0aux=aux.GYTREND0;
|
|
typeaux=aux.type;
|
|
if islogaux
|
|
yaux=exp(yaux+yauxss);
|
|
yauxss=exp(yauxss);
|
|
yaux=yaux-yauxss;
|
|
end
|
|
elseif type > 4
|
|
error('TYPE>4 requires auxiliary variable!')
|
|
end
|
|
if islog == 2
|
|
% construct loglevel out of growth rate
|
|
y = cumsum(y);
|
|
yss=0;
|
|
islog=1;
|
|
end
|
|
if islog == 1
|
|
y=exp(y+yss);
|
|
yss=exp(yss);
|
|
y=y-yss;
|
|
end
|
|
switch type
|
|
case 1
|
|
yass = yss*(exp(-GYTREND0*3)+exp(-GYTREND0*2)+exp(-GYTREND0)+1);
|
|
tmp = lagged(y,3)*exp(-GYTREND0*3)+lagged(y,2)*exp(-GYTREND0*2)+lagged(y,1)*exp(-GYTREND0)+y; % annualized level
|
|
ya = tmp(4:4:end);
|
|
case 2
|
|
yass = yss*(exp(-GYTREND0*3)+exp(-GYTREND0*2)+exp(-GYTREND0)+1)/4;
|
|
tmp = (lagged(y,3)*exp(-GYTREND0*3)+lagged(y,2)*exp(-GYTREND0*2)+lagged(y,1)*exp(-GYTREND0)+y)/4; % annualized level
|
|
ya = tmp(4:4:end);
|
|
case 3
|
|
yass=yss;
|
|
tmp = y;
|
|
ya = tmp(4:4:end);
|
|
case 4
|
|
yass = yss*(exp(-GYTREND0*3/2));
|
|
tmp = (lagged(y+yss,3)*exp(-GYTREND0*3).*lagged(y+yss,2)*exp(-GYTREND0*2).*lagged(y+yss,1)*exp(-GYTREND0).*(y+yss)).^(1/4); % annualized level
|
|
tmp = tmp - yass;
|
|
ya = tmp(4:4:end);
|
|
case 5
|
|
% nominal series
|
|
yn = (y+yss).*(yaux+yauxss) - yss.*yauxss;
|
|
[yna, ynass] = quarterly2annual(yn,yss.*yauxss,GYTREND0+GYTREND0aux,typeaux,0,0);
|
|
% real series
|
|
[yra, yrass] = quarterly2annual(yaux,yauxss,GYTREND0aux,typeaux,0,0);
|
|
% deflator
|
|
yass = ynass/yrass;
|
|
ya = (yna+ynass)./(yr+yrass)-yass;
|
|
case 6
|
|
% nominal series
|
|
yn = (y+yss).*(yaux+yauxss) - yss.*yauxss;
|
|
[yna, ynass] = quarterly2annual(yn,yss.*yauxss,GYTREND0+GYTREND0aux,typeaux,0,0);
|
|
% deflator
|
|
[pa, pass] = quarterly2annual(yaux,yauxss,GYTREND0aux,2,0,0);
|
|
% real series
|
|
yass = ynass/pass;
|
|
ya = (yna+ynass)./(pa+pass)-yass;
|
|
case 7
|
|
% nominal series
|
|
yn = (y+yss).*(yaux+yauxss) - yss.*yauxss;
|
|
[ya, yass] = quarterly2annual(yn,yss.*yauxss,GYTREND0+GYTREND0aux,typeaux,0,0);
|
|
GYTREND0=GYTREND0+GYTREND0aux;
|
|
otherwise
|
|
error('Wrong type input')
|
|
end
|
|
|
|
% annual growth rate
|
|
gyass = GYTREND0*4;
|
|
gya = (ya+yass)./(lagged(ya,1)+yass).*exp(4*GYTREND0)-1-gyass;
|
|
|
|
if islog
|
|
ya=log(ya+yass);
|
|
yass=log(yass);
|
|
ya=ya-yass;
|
|
end
|