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Add one-sided HP filter

time-shift
Johannes Pfeifer 2015-10-13 20:20:33 +02:00
parent 2c63ca8843
commit f7175745ac
7 changed files with 198 additions and 4 deletions
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7
license.txt
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@ -1,4 +1,4 @@
Format: http://www.debian.org/doc/packaging-manuals/copyright-format/1.0/
Format: http://www.debian.org/doc/packaging-manuals/copyright-format/1.0/
Upstream-Name: Dynare
Upstream-Contact: Dynare Team, whose members in 2015 are:
Stéphane Adjemian <stephane.adjemian@univ-lemans.fr>
@ -76,6 +76,11 @@ Copyright: 2008-2012 VZLU Prague, a.s.
2014 Dynare Team
License: GPL-3+
Files: matlab/one_sided_hp_filter.m
Copyright: 2010-2015 Alexander Meyer-Gohde
2015 Dynare Team
License: GPL-3+
Files: matlab/optimization/simpsa.m matlab/optimization/simpsaget.m matlab/optimization/simpsaset.m
Copyright: 2005 Henning Schmidt, FCC, henning@fcc.chalmers.se
2006 Brecht Donckels, BIOMATH, brecht.donckels@ugent.be

4
matlab/UnivariateSpectralDensity.m
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@ -109,7 +109,9 @@ ngrid = options_.hp_ngrid; %number of grid points
freqs = (0 : pi/(ngrid-1):pi)'; % grid on which to compute
tpos = exp( sqrt(-1)*freqs); %positive frequencies
tneg = exp(-sqrt(-1)*freqs); %negative frequencies
if options_.hp_filter == 0 && ~options_.bandpass.indicator %do not filter
if options_.one_sided_hp_filter
error('UnivariateSpectralDensity:: spectral density estimate not available with one-sided HP filter')
elseif options_.hp_filter == 0 && ~options_.bandpass.indicator %do not filter
filter_gain=ones(ngrid,1);
elseif ~(options_.hp_filter == 0 && ~options_.bandpass.indicator) && options_.bandpass.indicator %filter with bandpass
filter_gain = zeros(1,ngrid);

2
matlab/disp_moments.m
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@ -184,7 +184,7 @@ function y=get_filtered_time_series(y,m,options_)
if options_.hp_filter && ~options_.one_sided_hp_filter && ~options_.bandpass.indicator
[hptrend,y] = sample_hp_filter(y,options_.hp_filter);
elseif ~options_.hp_filter && options_.one_sided_hp_filter && ~options_.bandpass.indicator
error('disp_moments:: The one-sided HP filter is not yet available')
[hptrend,y] = one_sided_hp_filter(y,options_.one_sided_hp_filter);
elseif ~options_.hp_filter && ~options_.one_sided_hp_filter && options_.bandpass.indicator
data_temp=dseries(y,'0q1');
data_temp=baxter_king_filter(data_temp,options_.bandpass.passband(1),options_.bandpass.passband(2),200);

4
matlab/disp_th_moments.m
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@ -19,7 +19,9 @@ function oo_=disp_th_moments(dr,var_list,M_,options_,oo_)
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
nodecomposition = options_.nodecomposition;
if options_.one_sided_hp_filter
error(['disp_th_moments:: theoretical moments incompatible with one-sided HP filter. Use simulated moments instead'])
end
if size(var_list,1) == 0
var_list = M_.endo_names(1:M_.orig_endo_nbr, :);
end

113
matlab/one_sided_hp_filter.m Normal file
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@ -0,0 +1,113 @@
function [ytrend,ycycle]=one_sided_hp_filter(y,lambda,x_user,P_user,discard)
% function [ytrend,ycycle]=one_sided_hp_filter(y,lambda,x_user,P_user,discard)
% Conducts one-sided HP-filtering, derived using the Kalman filter
%
% Inputs:
% y [T*n] double data matrix in column format
% lambda [scalar] Smoothing parameter. Default value of 1600 will be used.
% x_user [2*n] double matrix with initial values of the state
% estimate for each variable in y. The underlying
% state vector is 2x1 for each variable in y.
% Default: use backwards extrapolations
% based on the first two observations
% P_user [n*1] struct structural array with n elements, each a two
% 2x2 matrix of intial MSE estimates for each
% variable in y.
% Default: matrix with large variances
% discard [scalar] number of initial periods to be discarded
% Default: 0
%
% Output:
% ytrend [(T-discard)*n] matrix of extracted trends
% ycycle [(T-discard)*n] matrix of extracted deviations from the extracted trends
%
% Algorithms:
%
% Implements the procedure described on p. 301 of Stock, J.H. and M.W. Watson (1999):
% "Forecasting inflation," Journal of Monetary Economics, vol. 44(2), pages 293-335, October.
% that states on page 301:
%
% "The one-sided HP trend estimate is constructed as the Kalman
% filter estimate of tau_t in the model:
%
% y_t=tau_t+epsilon_t
% (1-L)^2 tau_t=eta_t"
%
% The Kalman filter notation follows Chapter 13 of Hamilton, J.D. (1994).
% Time Series Analysis, with the exception of H, which is equivalent to his H'.
% Copyright (C) 200?-2015 Alexander Meyer-Gohde
% Copyright (C) 2015 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 < 2 || isempty(lambda)
lambda = 1600; %If the user didn't provide a value for lambda, set it to the default value 1600
end
[T,n] = size (y);% Calculate the number of periods and the number of variables in the series
%Set up state space
q=1/lambda; % the signal-to-noise ration: i.e. var eta_t / var epsilon_t
F=[2,-1;
1,0]; % state transition matrix
H=[1,0]; % observation matrix
Q=[q,0;
0,0]; % covariance matrix state equation errors
R=1; % variance observation equation error
for k=1:n %Run the Kalman filter for each variable
if nargin < 4 || isempty(x_user) %no intial value for state, extrapolate back two periods from the observations
x=[2*y(1,k)-y(2,k);
3*y(1,k)-2*y(2,k)];
else
x=x_user(:,k);
end
if nargin < 4 || isempty(P_user) %no initial value for the MSE, set a rather high one
P= [1e5 0;
0 1e5];
else
P=P_user{k};
end
for j=1:T %Get the estimates for each period
[x,P]=kalman_update(F,H,Q,R,y(j,k),x,P); %get new state estimate and update recursion
ytrend(j,k)=x(2);%second state is trend estimate
end
end
if nargout==2
ycycle=y-ytrend;
end
if nargin==5 %user provided a discard parameter
ytrend=ytrend(discard+1:end,:);%Remove the first "discard" periods from the trend series
if nargout==2
ycycle=ycycle(discard+1:end,:);
end
end
end
function [x,P]=kalman_update(F,H,Q,R,obs,x,P)
% Updates the Kalman filter estimation of the state and MSE
S=H*P*H'+R;
K=F*P*H';
K=K/S;
x=F*x+K*(obs -H*x); %State estimate
Temp=F-K*H;
P=Temp*P*Temp';
P=P+Q+K*R*K';%MSE estimate
end

1
tests/Makefile.am
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@ -11,6 +11,7 @@ MODFILES = \
moments/example1_hp_test.mod \
moments/example1_bp_test.mod \
moments/test_AR1_spectral_density.mod \
moments/example1_one_sided_hp_test.mod \
gsa/ls2003.mod \
gsa/ls2003a.mod \
gsa/cod_ML_morris/cod_ML_morris.mod \

71
tests/moments/example1_one_sided_hp_test.mod Normal file
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@ -0,0 +1,71 @@
/*
* Example 1 from F. Collard (2001): "Stochastic simulations with DYNARE:
* A practical guide" (see "guide.pdf" in the documentation directory).
*/
/*
* Copyright (C) 2001-2010 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/>.
*/
var y, c, k, a, h, b;
varexo e, u;
parameters beta, rho, alpha, delta, theta, psi, tau;
alpha = 0.36;
rho = 0.95;
tau = 0.025;
beta = 0.99;
delta = 0.025;
psi = 0;
theta = 2.95;
phi = 0.1;
model;
c*theta*h^(1+psi)=(1-alpha)*y;
k = beta*(((exp(b)*c)/(exp(b(+1))*c(+1)))
*(exp(b(+1))*alpha*y(+1)+(1-delta)*k));
y = exp(a)*(k(-1)^alpha)*(h^(1-alpha));
k = exp(b)*(y-c)+(1-delta)*k(-1);
a = rho*a(-1)+tau*b(-1) + e;
b = tau*a(-1)+rho*b(-1) + u;
end;
initval;
y = 1.08068253095672;
c = 0.80359242014163;
h = 0.29175631001732;
k = 11.08360443260358;
a = 0;
b = 0;
e = 0;
u = 0;
end;
shocks;
var e; stderr 0.009;
var u; stderr 0.009;
var e, u = phi*0.009*0.009;
end;
steady(solve_algo=4,maxit=1000);
options_.hp_ngrid=2048*4;
stoch_simul(order=1,nofunctions,one_sided_hp_filter=1600,irf=0,periods=5000);