PhillipsPerron test for one unit root
[h,pValue,stat,cValue,reg] = pptest(y
) [h,pValue,stat,cValue,reg] = pptest(y
,'ParameterName'
,ParameterValue
,...)
PhillipsPerron tests assess the null hypothesis of a unit root
in a univariate time series y
. All tests
use the model:
y_{t} = c + δt + a y_{t – 1} + e(t).
The null hypothesis restricts a = 1. Variants
of the test, appropriate for series with different growth characteristics,
restrict the drift and deterministic trend coefficients, c and δ,
respectively, to be 0. The tests use modified DickeyFuller statistics
(see adftest
) to account for serial correlations
in the innovations process e(t).

Vector of timeseries data. The last element is the most recent
observation. 

Scalar or vector of nonnegative integers indicating the number of autocovariance lags to include in the NeweyWest estimator of the longrun variance. For best results, give a suitable value for Default: 

Character vector, such as
Default: 

Character vector, such as
Default: 

Scalar or vector of nominal significance levels for the tests.
Set values between Default: 

Vector of Boolean decisions for the tests, with length equal
to the number of tests. Values of  

Vector of pvalues of the test statistics, with length equal to the number of tests. pvalues are lefttail probabilities. When test statistics are outside tabulated critical values,
 

Vector of test statistics, with length equal to the number of tests. Statistics are computed using OLS estimates of the coefficients in the alternative model.  

Vector of critical values for the tests, with length equal to the number of tests. Values are for lefttail probabilities.  

Structure of regression statistics for the OLS estimation of coefficients in the alternative model. The number of records equals the number of tests. Each record has the following fields:

pptest
performs a leastsquares regression
to estimate coefficients in the null model.
The tests use modified DickeyFuller statistics (see adftest
) to account for serial correlations
in the innovations process e(t).
PhillipsPerron statistics follow nonstandard distributions under
the null, even asymptotically. Critical values for a range of sample
sizes and significance levels have been tabulated using Monte Carlo
simulations of the null model with Gaussian innovations and five million
replications per sample size. pptest
interpolates
critical values and pvalues from the tables. Tables
for tests of type 't1'
and 't2'
are
identical to those for adftest
.
[1] Davidson, R., and J. G. MacKinnon. Econometric Theory and Methods. Oxford, UK: Oxford University Press, 2004.
[2] Elder, J., and P. E. Kennedy. “Testing for Unit Roots: What Should Students Be Taught?” Journal of Economic Education. Vol. 32, 2001, pp. 137–146.
[3] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
[4] Newey, W. K., and K. D. West. “A Simple Positive Semidefinite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica. Vol. 55, 1987, pp. 703–708.
[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.
[8] Schwert, W. “Tests for Unit Roots: A Monte Carlo Investigation.” Journal of Business and Economic Statistics. Vol. 7, 1989, pp. 147–159.
[9] White, H., and I. Domowitz. “Nonlinear Regression with Dependent Observations.” Econometrica. Vol. 52, 1984, pp. 143–162.