1function o = baxter_king_filter_(o, high_frequency, low_frequency, K) % --*-- Unitary tests --*--
2
3% Implementation of Baxter and King (1999) band pass filter for dseries objects. The code is adapted from
4% the one provided by Baxter and King. This filter isolates business cycle fluctuations with a period of length
5% ranging between high_frequency to low_frequency (quarters).
6%
7% INPUTS
8%  - o                  dseries object.
9%  - high_frequency     positive scalar, period length (default value is 6).
10%  - low_frequency      positive scalar, period length (default value is 32).
11%  - K                  positive scalar integer, truncation parameter (default value is 12).
12%
13% OUTPUTS
14%  - o                  dseries object.
15%
16% REMARKS
17% This filter use a (symmetric) moving average smoother, so that K observations at the beginning and at the end of the
18% sample are lost in the computation of the filter.
19
20% Copyright (C) 2013-2017 Dynare Team
21%
22% This file is part of Dynare.
23%
24% Dynare is free software: you can redistribute it and/or modify
25% it under the terms of the GNU General Public License as published by
26% the Free Software Foundation, either version 3 of the License, or
27% (at your option) any later version.
28%
29% Dynare is distributed in the hope that it will be useful,
30% but WITHOUT ANY WARRANTY; without even the implied warranty of
31% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
32% GNU General Public License for more details.
33%
34% You should have received a copy of the GNU General Public License
35% along with Dynare.  If not, see <http://www.gnu.org/licenses/>.
36
37if nargin<4 || isempty(K)
38    K = 12;
39    if nargin<3 || isempty(low_frequency)
40        % Set default number of periods corresponding to the lowest frequency.
41        low_frequency = 32;
42        if nargin<2 || isempty(high_frequency)
43            % Set default number of periods corresponding to the highest frequency.
44            high_frequency = 6;
45            if nargin<1
46                error('dseries::baxter_king_filter: I need at least one argument')
47            end
48        else
49            if high_frequency<2
50                error('dseries::baxter_king_filter: Second argument must be greater than 2!')
51            end
52            if high_frequency>low_frequency
53                error('dseries::baxter_king_filter: Second argument must be smaller than the third argument!')
54            end
55        end
56    end
57end
58
59% translate periods into frequencies.
60hf=2.0*pi/high_frequency;
61lf=2.0*pi/low_frequency;
62
63% Set weights for the band-pass filter's lag polynomial.
64weights = zeros(K+1,1); lpowers = transpose(1:K);
65weights(2:K+1) = (sin(lpowers*hf)-sin(lpowers*lf))./(lpowers*pi);
66weights(1) = (hf-lf)/pi;
67
68% Set the constraint on the sum of weights.
69if low_frequency>1000
70    % => low pass filter.
71    sum_of_weights_constraint = 1.0;
72else
73    sum_of_weights_constraint = 0.0;
74end
75
76% Compute the sum of weights.
77sum_of_weights = weights(1) + 2*sum(weights(2:K+1));
78
79% Correct the weights.
80weights = weights + (sum_of_weights_constraint - sum_of_weights)/(2*K+1);
81
82% Weights are symmetric!
83weights = [flipud(weights(2:K+1)); weights];
84
85tmp = zeros(size(o.data));
86
87% Filtering step.
88for t = K+1:nobs(o)-K
89    tmp(t,:)  = weights'*o.data(t-K:t+K,:);
90end
91
92% Update dseries object.
93o.data = tmp(K+1:end-K,:);
94init = firstdate(o)+K;
95o.dates = init:init+(nobs(o)-1);
96for i=1:vobs(o)
97    if isempty(o.ops{i})
98        o.ops(i) = {sprintf('baxter_king_filter(%s, %s, %s, %s)', ...
99                            o.name{i}, ...
100                            num2str(high_frequency), ...
101                            num2str(low_frequency), ...
102                            num2str(K))};
103    else
104        o.ops(i) = {sprintf('baxter_king_filter(%s, %s, %s, %s)', ...
105                            o.ops{i}, ...
106                            num2str(high_frequency), ...
107                            num2str(low_frequency), ...
108                            num2str(K))};
109    end
110end
111
112
113%@test:1
114%$ plot_flag = false;
115%$
116%$ % Create a dataset.
117%$ e = .2*randn(200,1);
118%$ u = randn(200,1);
119%$ stochastic_trend = cumsum(e);
120%$ deterministic_trend = .1*transpose(1:200);
121%$ x = zeros(200,1);
122%$ for i=2:200
123%$    x(i) = .75*x(i-1) + e(i);
124%$ end
125%$ y = x + stochastic_trend + deterministic_trend;
126%$
127%$ % Test the routine.
128%$ try
129%$     ts = dseries(y,'1950Q1');
130%$     ts.baxter_king_filter_();
131%$     xx = dseries(x,'1950Q1');
132%$     t(1) = 1;
133%$ catch
134%$     t(1) = 0;
135%$ end
136%$
137%$ if t(1)
138%$     t(2) = dassert(ts.freq,4);
139%$     t(3) = dassert(ts.init.freq,4);
140%$     t(4) = dassert(ts.init.time,[1953, 1]);
141%$     t(5) = dassert(ts.vobs,1);
142%$     t(6) = dassert(ts.nobs,176);
143%$     t(7) = dassert(ts.name{1},'Variable_1');
144%$     t(8) = dassert(ts.ops{1},'baxter_king_filter(Variable_1, 6, 32, 12)');
145%$ end
146%$
147%$ % Show results
148%$ if plot_flag
149%$     plot(xx(ts.dates).data,'-k');
150%$     hold on
151%$     plot(ts.data,'--r');
152%$     hold off
153%$     axis tight
154%$     id = get(gca,'XTick');
155%$     set(gca,'XTickLabel',strings(ts.dates(id)));
156%$     legend({'Stationary component of y', 'Filtered y'})
157%$     print('-depsc2','../doc/dynare.plots/BaxterKingFilter.eps')
158%$     system('convert -density 300 ../doc/dynare.plots/BaxterKingFilter.eps ../doc/dynare.plots/BaxterKingFilter.png');
159%$     system('convert -density 300 ../doc/dynare.plots/BaxterKingFilter.eps ../doc/dynare.plots/BaxterKingFilter.pdf');
160%$     system('convert -density 300 ../doc/dynare.plots/BaxterKingFilter.eps ../doc/dynare.plots/BaxterKingFilter.jpg');
161%$ end
162%$
163%$ T = all(t);
164%@eof:1
165