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    %% Test for the Degree of Integration  
% Conduct paired integration and stationarity tests on two time series and
% their differences.   

% Copyright 2015 The MathWorks, Inc.


%% 
% Load the Nelson-Plosser data, and extract the series of real GNP, |GNPR|,
% and consumer price index, |CPI|. 
load Data_NelsonPlosser		
X = DataTable(:,{'GNPR','CPI'});  
%%
% |X| is a tabular array containing the variables |GNPR| and |CPI|.
%% 
% Set the integration and stationarity test parameters. 
I.names = {'lags','model'};
I.vals = {1,'TS'};

S.names = {'trend'};
S.vals = {true};  

%%
% The integration test is the default (|adftest|), augmented with one lagged
% difference term and a trend-stationary alternative. The stationarity test
% is the default (|kpsstest|) with a trend.  

%% 
% Conduct the integration and stationarity tests on the variables and their
% first differences, specified using |numDiffs|. 
i10test(X,'numDiffs',1,'itest','adf','iparams',I,...
        'stest','kpss','sparams',S) 

%%
% The warnings indicate that the p-values are very large or small for some
% of the tests (that is, they are outside the Monte Carlo simulated tables).
% For each original series, a unit root is not rejected (|H = 0| for |I(1)|),
% and stationarity is rejected (|H = 1| for |I(0)|). For the differenced
% series, a unit root is rejected and stationarity is not rejected. 

%%
% At the given parameter settings, the tests suggest that both series have
% one degree of integration.