Conduct paired integration and stationarity tests on two time series using the default tests and settings.

Load the Nelson-Plosser data, and extract the series of real GNP, `GNPR`

, and consumer price index, `CPI`

.

`X`

is a matrix containing the data for the variables `GNPR`

and `CPI`

.

Conduct the default integration (`adftest`

) stationarity (`kpsstest`

) tests on the two time series.

Warning: Test statistic #1 above tabulated critical values:
maximum p-value = 0.999 reported.
Warning: Test statistic #1 above tabulated critical values:
minimum p-value = 0.010 reported.
Warning: Test statistic #1 above tabulated critical values:
maximum p-value = 0.999 reported.
Warning: Test statistic #1 above tabulated critical values:
minimum p-value = 0.010 reported.
Test Results
I(1) I(0)
======================
var1 0 1
0.9990 0.0100
----------------------
var2 0 1
0.9990 0.0100
----------------------

The warnings indicate that the p-values are very large for `adftest`

and very small for `kpsstest`

(that is, they are outside the Monte Carlo simulated tables). For both series, a unit root is not rejected (`H = 0`

for `I(1)`

), and stationarity is rejected (`H = 1`

for `I(0)`

).

Conduct paired integration and stationarity tests on two time series and their differences.

Load the Nelson-Plosser data, and extract the series of real GNP, `GNPR`

, and consumer price index, `CPI`

.

`X`

is a tabular array containing the variables `GNPR`

and `CPI`

.

Set the integration and stationarity test parameters.

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`

.

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.
Test Results
I(1) I(0)
======================
GNPR 0 1
0.8760 0.0100
D1GNPR 1 0
0.0054 0.1000
----------------------
CPI 0 1
0.9799 0.0100
D1CPI 1 0
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). 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.

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`

.

`X`

is a tabular array containing the variables `GNPR`

and `CPI`

.

Set the integration and stationarity test parameters.

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

.

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.