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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
% 8 annual ratio [e.g. trade balance to GDP]
% 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 © 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 <https://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)./(yra+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;
case 8
% numerator
yn = y;
[yna, ynass] = quarterly2annual(yn,yss,GYTREND0,typeaux(1),0,0);
% denominator
yd = yaux;
[yda, ydass] = quarterly2annual(yd,yauxss,GYTREND0aux,typeaux(2),0,0);
% ratio
yass = ynass/ydass;
ya = (yna+ynass)./(yda+ydass)-yass;
GYTREND0 = GYTREND0 - GYTREND0aux;
otherwise
error('Wrong type input')
end
% annual growth rate
% gyass = GYTREND0*4; % this is for log diff
gyass = exp(4*GYTREND0)-1; % this is for exact growth rate definition
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
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