149 lines
4.8 KiB
Matlab
149 lines
4.8 KiB
Matlab
function ts = baxter_king_filter(ts, high_frequency, low_frequency, K) % --*-- Unitary tests --*--
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% ts = baxter_king_filter(ts, high_frequency, low_frequency, K)
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%
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% Implementation of Baxter and King (1999) band pass filter for dseries objects. The code is adapted from
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% the one provided by Baxter and King. This filter isolates business cycle fluctuations with a period of length
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% ranging between high_frequency to low_frequency (quarters).
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%
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% INPUTS
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% o ts dseries object.
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% o high_frequency positive scalar, period length (default value is 6).
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% o low_frequency positive scalar, period length (default value is 32).
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% o K positive scalar integer, truncation parameter (default value is 12).
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%
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% OUTPUTS
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% o ts dseries object.
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%
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% REMARKS
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% This filter use a (symmetric) moving average smoother, so that K observations at the beginning and at the end of the
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% sample are lost in the computation of the filter.
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% Copyright (C) 2013 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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if nargin<4 || isempty(truncature)
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K = 12;
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if nargin<3 || isempty(low_frequency)
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% Set default number of periods corresponding to the lowest frequency.
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low_frequency = 32;
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if nargin<2 || isempty(high_frequency)
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% Set default number of periods corresponding to the highest frequency.
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high_frequency = 6;
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if nargin<1
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error('dseries::baxter_king_filter: I need at least one argument')
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end
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else
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if high_frequency<2
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error('dseries::baxter_king_filter: Second argument must be greater than 2!')
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end
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if high_frequency>low_frequency
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error('dseries::baxter_king_filter: Second argument must be smaller than the third argument!')
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end
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end
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end
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end
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% translate periods into frequencies.
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hf=2.0*pi/high_frequency;
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lf=2.0*pi/low_frequency;
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% Set weights for the band-pass filter's lag polynomial.
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weights = zeros(K+1,1); lpowers = transpose(1:K);
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weights(2:K+1) = (sin(lpowers*hf)-sin(lpowers*lf))./(lpowers*pi);
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weights(1) = (hf-lf)/pi;
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% Set the constraint on the sum of weights.
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if low_frequency>1000
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% => low pass filter.
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sum_of_weights_constraint = 1.0;
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else
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sum_of_weights_constraint = 0.0;
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end
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% Compute the sum of weights.
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sum_of_weights = weights(1) + 2*sum(weights(2:K+1));
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% Correct the weights.
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weights = weights + (sum_of_weights_constraint - sum_of_weights)/(2*K+1);
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% Weights are symmetric!
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weights = [flipud(weights(2:K+1)); weights];
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tmp = zeros(size(ts.data));
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% Filtering step.
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for t = K+1:ts.nobs-K
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tmp(t,:) = weights'*ts.data(t-K:t+K,:);
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end
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% Update dseries object.
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ts.data = tmp(K+1:end-K,:);
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ts.nobs = ts.nobs-2*K;
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ts.init = ts.init+K;
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ts.dates = ts.init:ts.init+(ts.nobs-1);
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%@test:1
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%$ plot_flag = 0;
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%$
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%$ % Create a dataset.
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%$ e = .2*randn(200,1);
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%$ u = randn(200,1);
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%$ stochastic_trend = cumsum(e);
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%$ deterministic_trend = .1*transpose(1:200);
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%$ x = zeros(200,1);
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%$ for i=2:200
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%$ x(i) = .75*x(i-1) + e(i);
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%$ end
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%$ y = x + stochastic_trend + deterministic_trend;
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%$
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%$ % Test the routine.
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%$ try
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%$ ts = dseries(y,'1950Q1');
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%$ ts = ts.baxter_king_filter();
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%$ xx = dseries(x,'1950Q1');
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%$ t(1) = 1;
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%$ catch
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%$ t(1) = 0;
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%$ end
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%$
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%$ if t(1)
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%$ t(2) = dyn_assert(ts.freq,4);
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%$ t(3) = dyn_assert(ts.init.freq,4);
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%$ t(4) = dyn_assert(ts.init.time,[1953, 1]);
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%$ t(5) = dyn_assert(ts.vobs,1);
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%$ t(6) = dyn_assert(ts.nobs,176);
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%$ end
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%$
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%$ % Show results
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%$ if plot_flag
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%$ plot(xx(ts.dates).data,'-k');
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%$ hold on
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%$ plot(ts.data,'--r');
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%$ hold off
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%$ axis tight
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%$ id = get(gca,'XTick');
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%$ set(gca,'XTickLabel',strings(ts.dates(id)));
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%$ legend({'Stationary component of y', 'Filtered y'})
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%$ print('-depsc2','../doc/dynare.plots/BaxterKingFilter.eps')
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%$ system('convert -density 300 ../doc/dynare.plots/BaxterKingFilter.eps ../doc/dynare.plots/BaxterKingFilter.png');
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%$ system('convert -density 300 ../doc/dynare.plots/BaxterKingFilter.eps ../doc/dynare.plots/BaxterKingFilter.pdf');
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%$ system('convert -density 300 ../doc/dynare.plots/BaxterKingFilter.eps ../doc/dynare.plots/BaxterKingFilter.jpg');
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%$ end
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%$
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%$ T = all(t);
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%@eof:1 |