File
joint_gap_indicators.m
Name
joint_gap_indicators
Synopsis
joint_gap_indicators - Calculates the signal-to-noise (SNR) ratio and the number of predicted crises of joint signal indicators for particular thresholds based on Borio et al. (2009).
Introduction
NOTE: PART OF A SET OF 2 RELATED FILES:
Borio (2009) construct macroeconomic early warning indicators to predict banking sector crises by extending the framework of Borio and Lowe (2004). The three indicators used are the property price gap, the (real) equity price gap, and the credit gap. This approach is grounded in the endogenous-cycle view of financial instability. The authors argue that the coexistence of unusually rapid credit growth and asset prices indicate the build-up of financial imbalances that raise the likelihood of subsequent financial distress.
License
=============================================================================
Copyright 2011, Dimitrios Bisias, Andrew W. Lo, and Stavros Valavanis
COPYRIGHT STATUS: This work was funded in whole or in part by the Office of
Financial Research under U.S. Government contract TOSOFR-11-C-0001, and is,
therefore, subject to the following license: The Government is granted for
itself and others acting on its behalf a paid-up, nonexclusive, irrevocable,
worldwide license to reproduce, prepare derivative works,
distribute copies to the public, perform and display the work.
All other rights are reserved by the copyright owner.
THIS SOFTWARE IS PROVIDED "AS IS". YOU ARE USING THIS SOFTWARE AT YOUR OWN RISK. ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS, CONTRIBUTORS, OR THE UNITED STATES GOVERNMENT BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
=============================================================================
Inputs
Outputs
Code
% Run warning message
warning('OFRwp0001:UntestedCode', ...
['This version of the source code is very preliminary, ' ...
'and has not been thoroughly tested. Users should not rely on ' ...
'these calculations.']);
num_years = size(indicators_series,1);
buffer_length = 10;
successes = 0;
false_alarms = 0;
missed_crises = 0;
negative_successes = 0;
% We need to have at least 10 years of data
if num_years < buffer_length
error('Not enought years of data.');
end
% We 'll run the HP filters from year buffer_length to num_years-horizon
gaps = zeros(num_years-buffer_length+1-horizon,2);
for t=buffer_length:num_years-horizon
for i=1:2
trend = hpfilter(indicators_series(1:t,i),1600);
% Gap is the difference of the value of the time_series and the
% trend
gaps(t-buffer_length+1,i) = trend(t) - indicators_series(t,i);
end
% If both of the gaps are greater than the corresponding thresholds
% then we have a signal that there will be a crisis in the next horizon
% years
if sum(gaps(t-buffer_length+1,:)>thresholds')==2
if sum(is_crisis_series(t+1:t+horizon))>0
successes = successes + 1;
else
false_alarms = false_alarms+1;
end
else
% No crisis is predicted for the next horizon years
if sum(is_crisis_series(t+1:t+horizon))>0
missed_crises = missed_crises + 1;
else
negative_successes = negative_successes+1;
end
end
end
type_I_error = 0;
type_II_error = 0;
if (false_alarms + negative_successes) ~=0
type_II_error = false_alarms/(false_alarms + negative_successes);
end
if (missed_crises + successes) ~=0
type_I_error = missed_crises/(missed_crises + successes);
end
nts = type_II_error/(1-type_I_error);
num_predicted_crises = successes;
Examples
NOTE: Numbers used in the examples are arbitrary valid values.
They do not necessarily represent a realistic or plausible scenario.
indicators_series = ...
[.17 .18 .15 .30 .42 .53 .32 .36 .34 .23 .21 .80 .10 .05 .22; ...
130 132 120 124 130 124 140 165 180 140 130 120 132 129 110]';
thresholds = [.1; 20] ;
horizon = 3;
is_crisis_series = [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]';
[nts num_predicted_crises] = joint_gap_indicators(indicators_series, ...
thresholds, is_crisis_series, horizon);
References