# i10test

Paired integration and stationarity tests

## Description

`[`

displays, at the command window, the results
of paired integration and stationarity tests on the variables in the input matrix of time
series data. Row labels in the display table are variable names and their differences.
Column labels are `H`

,`PValue`

]
= i10test(`X`

)`I(1)`

and `I(0)`

, respectively, to
indicate the null hypothesis of the test.

The function also returns the matrix of test rejection decisions and associated
*p*-values for the test statistics.

displays the results of paired integration and stationarity tests on all the variables of
an input table or timetable. The function also returns a table containing variables for
the test rejection decisions and associated `DecisionTbl`

= i10test(`Tbl`

)*p*-values for the test
statistics.

To select a subset of variables in `Tbl`

to test, use the
`DataVariables`

name-value argument.

`[___] = i10test(___,`

specifies options using one or more name-value arguments in
addition to any of the input argument combinations in previous syntaxes.
`Name=Value`

)`i10test`

returns the output argument combination for the
corresponding input arguments. For example, `i10test(Tbl,NumDiffs=1,DataVariables=1:5)`

tests the first 5 variables in the input table `Tbl`

, and tests their
first difference.

## Examples

## Input Arguments

## Output Arguments

## Tips

Kwiatkowski, Phillips, Schmidt, and Shin [1], and other references, suggest paired integration and stationarity tests as a method for mutual confirmation of individual test results. However, different integration test results can disagree on the same set of data, different stationarity test results can disagree, and stationarity tests can fail to confirm integration tests. Still, Amano and van Norden [2], Burke [3], and other references, perform Monte Carlo studies that suggest that paired testing is generally more reliable than using either type of test alone.

## References

[1] Kwiatkowski, D., P. C.
B. Phillips, P. Schmidt, and Y. Shin. “Testing the Null Hypothesis of Stationarity against the
Alternative of a Unit Root.” *Journal of Econometrics*. Vol. 54, 1992, pp.
159–178.

[2] Amano, R. A., and S. van Norden. "Unit Root Tests and the Burden of Proof." Bank of Canada. Working paper 92–7, 1992.

[3] Burke, S. P. "Confirmatory Data Analysis: The Joint Application of Stationarity and Unit Root Tests." University of Reading, UK. Discussion paper 20, 1994.

## Version History

**Introduced in R2012a**