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    %% Inspect Real U.S. GNP Model for Instability
% Apply recursive regressions using nested windows to look for
% instability in an explanatory model of real GNP for a period spanning
% World War II.
%%
% Load the Nelson-Plosser data set.
load Data_NelsonPlosser
%%
% The time series in the data set contain annual, macroeconomic
% measurements from 1860 to 1970. For more details, a list of variables,
% and descriptions, enter |Description| in the command line.  
%%
% Several series have missing data.  Focus the sample to measurements from
% 1915 to 1970.  Identify the breakpoint index corresponding to 1945, the end of the
% war.
span = (1915 <= dates) & (dates <= 1970);
bp = find(dates(span) == 1945);
%%
% Consider the multiple linear regression model 
%
% $$\texttt{GNPR}_t=\beta_0+\beta_1\texttt{IPI}_t+\beta_2\texttt{E}_t+\beta_3\texttt{WR}_t.$$
%
%%
% Collect the model variables into a tabular array. Position the predictors
% in the first three columns, and the response in the last column.  Compute
% the number of coefficients in the model.
Mdl = DataTable(span,[4,5,10,1]);
numCoeff = size(Mdl,2); % Three predictors and an intercept
%%
% Estimate the coefficients using recursive regressions, and return
% separate plots for the iterative estimates.  Identify the iteration
% corresponding to the end of the war.
recreg(Mdl);
bpIter = bp - numCoeff
%%
% By default, |recreg| forms the subsamples using nested windows.  The end
% of the war (1945) occurs at the 27th iteration.
%%
% All coefficients show some initial, transient instability during the the
% "burn-in" period (see <docid:econ_ug.bu55p4z-5>).  The plot of |WR| seems
% stable since the line is relatively flat.  However, the plots of |E|,
% |IPI|, and the intercept (|Const|) show instability, particularly just
% after iteration 27.