# pptest

Phillips-Perron test for one unit root

## Syntax

## Description

returns the
rejection decision `h`

= pptest(`y`

)`h`

from conducting the Phillips-Perron test for a unit
root in the univariate time series `y`

.

returns the table `StatTbl`

= pptest(`Tbl`

)`StatTbl`

containing variables for the test results,
statistics, and settings from conducting the Phillips-Perron test on the last variable of
the input table or timetable `Tbl`

. To select a different variable in
`Tbl`

to test, use the `DataVariable`

name-value
argument.

`[___] = pptest(___,`

uses additional options specified by one or more name-value arguments, using any input-argument combination in the previous syntaxes. `Name=Value`

)`pptest`

returns the output-argument combination for the corresponding input arguments.

Some options control the number of tests to conduct. The following conditions apply when
`pptest`

conducts multiple tests:

For example, ```
pptest(Tbl,DataVariable="GDP",Alpha=0.025,Lags=[0
1])
```

conducts two tests, at a level of significance of 0.025, on the variable
`GDP`

of the table `Tbl`

. The first test includes
`0`

autocovariance lags in the Newey-West covariance estimator and the
second test includes `1`

autocovariance lags.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

To draw valid inferences from a Phillips-Perron test, you must determine a suitable value for the

`Lags`

argument. The following methods help determine a suitable value:Begin by setting a small value and then evaluate the sensitivity of the results by adding more lags.

Inspect sample autocorrelations of

*y*−_{t}*y*_{t−1}; slow rates of decay require more lags.

The Newey-West estimator is consistent when the number of lags is

*O*(*T*^{1/4}), where*T*is the effective sample size, adjusted for lag and missing values. For more details, see [9] and [5].With a specific testing strategy in mind, determine the value of

`Model`

by the growth characteristics of*y*. If you include too many regressors (see_{t}`Lags`

), the test loses power; if you include too few regressors, the test is biased towards favoring the null model [2]. In general, if a series grows, the`"TS"`

model (see`Model`

) provides a reasonable trend-stationary alternative to a unit-root process with drift. If a series is does not grow, the`"AR"`

and`"ARD"`

models provide reasonable stationary alternatives to a unit-root process without drift. The`"ARD"`

alternative model has a mean of*c*/(1 –*a*); the`"AR"`

alternative model has mean 0.

## Algorithms

In general, when a time series is lagged, the sample size is reduced. Without a presample, if

*y*is defined for_{t}*t*= 1,…,*T*, the lag*k*series*y*_{t–k}is defined for*t*=*k*+1,…,*T*. Consequently, the effective sample size of the common time base is*T*−*k*.To account for serial correlations in the innovations process

*ε*,_{t}`pptest`

uses modified Dickey-Fuller statistics (see`adftest`

).Phillips-Perron statistics

`stat`

follow nonstandard distributions under the null, even asymptotically.`pptest`

uses tabulated critical values, generated by Monte Carlo simulations, for a range of sample sizes and significance levels of the null model with Gaussian innovations and five million replications per sample size.`pptest`

interpolates critical values`cValue`

and*p*-values`pValue`

from the tables. Tables for tests of`Test`

types`"t1"`

and`"t2"`

are identical to those for`adftest`

.

## References

[1] Davidson, R., and J. G. MacKinnon. *Econometric Theory and Methods*. Oxford, UK: Oxford University Press, 2004.

[3] Hamilton, James D. *Time Series Analysis*. Princeton, NJ: Princeton University Press, 1994.

[5] Perron, P. "Trends and Random Walks in Macroeconomic Time
Series: Further Evidence from a New Approach." *Journal of Economic Dynamics and
Control*. Vol. 12, 1988, pp. 297–332.

[6] Phillips, P. "Time Series Regression with a Unit Root."
*Econometrica*. Vol. 55, 1987, pp. 277–301.

[7] Phillips, P., and P. Perron. "Testing for a Unit Root in Time
Series Regression." *Biometrika*. Vol. 75, 1988, pp.
335–346.

[9] White, H., and I. Domowitz. "Nonlinear Regression with
Dependent Observations." *Econometrica*. Vol. 52, 1984, pp.
143–162.

## Version History

**Introduced in R2009b**