Conduct paired integration and stationarity tests on two time series and their differences. Turn the results display off, and return the test decisions and p-values.

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};

Conduct the integration and stationarity tests on the variables and their first differences, specified using `numDiffs`.

[H,PValue] = i10test(X,'numDiffs',1,'itest','adf',...
'iparams',I,'stest','kpss',...
'sparams',S,'display','off')

Warning: Test statistic #1 above tabulated critical values:
minimum p-value = 0.010 reported.
Warning: Test statistic #1 below tabulated critical values:
maximum p-value = 0.100 reported.
Warning: Test statistic #1 above tabulated critical values:
minimum p-value = 0.010 reported.
Warning: Test statistic #1 below tabulated critical values:
minimum p-value = 0.001 reported.
H =
0 1
1 0
0 1
1 0
PValue =
0.8760 0.0100
0.0054 0.1000
0.9799 0.0100
0.0010 0.0568

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). The test decisions and p-values are stored in `H` and `PValue`, respectively.

For each original series, a unit root is not rejected (`H = 0`), and stationarity is rejected (`H = 1`), as indicated in the first and third rows of the output `H`. For each differenced series, a unit root is rejected (`H = 1`), and stationarity is not rejected (`H = 0`), as indicated in the second and fourth rows of the output `H`.

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