File
fit_ar_model.m
Name
fit_ar_model
Synopsis
fit_ar_model - Fits an AR model to the y-series representing GDP data. It selects the order that is less than max_order and minimizes the BIC.
Introduction
NOTE: PART OF A SET OF 2 RELATED FILES:
Alfaro and Drehmann (2009) propose a macroeconomic stress test using a simple AR model of GDP growth which is assumed to depend only on its past behavior. The reason the authors focus on GDP is they observe that domestic macroeconomic conditions as measured by GDP growth typically weaken ahead of banking crises. Furthermore, output drops substantially in nearly all of the observed crises once stress emerges. Their approach to stress testing uses this as a starting point to construct GDP scenarios, independently of whether falls in output truly reflect or cause crises. Their guiding principle in creating their GDP shocks is that stress scenarios should be severe yet plausible.
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.']);
n = length(y_series);
BIC = zeros(max_order,1);
betas = zeros(max_order+1,max_order);
for order = 1:max_order
% Form the response variables and covariates
y = y_series(order+1:end);
X = zeros(n-order,order);
for j = 1:order
X(:,j) = y_series(order+1-j:end-j);
end
whichstats = {'beta', 'r'};
% The constant term is added automatically
stats = regstats(y,X,'linear',whichstats);
betas(1:order+1,order) = stats.beta;
r = stats.r;
% Instead of s^2 we use the maximum likelihood estimate of variance
% i.e. we divide r'*r by n instead of n - num_regressors
BIC(order)=n*log(r'*r/n)+order*log(n);
end
% Find the minimum bic and the corresponding regressor coefficients
[bic_min, min_order] = min(BIC);
regressor_coefficients = betas(1:min_order+1,min_order);
order = min_order;
Examples
NOTE: Numbers used in the examples are arbitrary valid values.
They do not necessarily represent a realistic or plausible scenario.
y_series = [5.3, 3.4, -1.1, 2.3, 2.3, 4.8, 3.3, 4.5]';
max_order = 3;
[regressor_coefficients, order] = fit_ar_model(y_series, max_order);
References