Phillips-Perron test for one unit root
[h,pValue,stat,cValue,reg] = pptest(y) [h,pValue,stat,cValue,reg] = pptest(y,'ParameterName',ParameterValue,...)
Phillips-Perron tests assess the null hypothesis of a unit root in a univariate time series y. All tests use the model:
yt = c + δt + a yt – 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 Dickey-Fuller statistics (see adftest) to account for serial correlations in the innovations process e(t).
Vector of time-series data. The last element is the most recent observation. NaNs indicating missing values are removed.
Scalar or vector of nonnegative integers indicating the number of autocovariance lags to include in the Newey-West estimator of the long-run variance.
For best results, give a suitable value for lags. For information on selecting lags, see Determining an Appropriate Number of Lags.
String or cell vector of strings indicating the model variant. Values are:
String or cell vector of strings indicating the test statistic. Values are:
Scalar or vector of nominal significance levels for the tests. Set values between 0.001 and 0.999.
Vector of Boolean decisions for the tests, with length equal to the number of tests. Values of h equal to 1 indicate rejection of the unit-root null in favor of the alternative model. Values of h equal to 0 indicate a failure to reject the unit-root null.
Vector of p-values of the test statistics, with length equal to the number of tests. p-values are left-tail probabilities.
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 left-tail 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:
The Phillips-Perron model is
yt = c + δt + a yt – 1 + e(t).
where e(t) is the innovations process.
The test assesses the null hypothesis under the model variant appropriate for series with different growth characteristics (c = 0 or δ = 0).
Test GDP data for a unit root using a trend-stationary alternative with 0, 1, and 2 lags for the Newey-West estimator.
Load the GDP data set.
load Data_GDP logGDP = log(Data);
Perform the Phillips-Perron test including 0, 1, and 2 autocovariance lags in the Newey-West robust covariance estimator.
h = pptest(logGDP,'model','TS','lags',0:2)
h = 0 0 0
Each test returns h = 0, which means the test fails to reject the unit-root null hypothesis for each set of lags. Therefore, there is not enough evidence to suggest that log GDP is trend stationary.
pptest performs a least-squares regression to estimate coefficients in the null model.
The tests use modified Dickey-Fuller statistics (see adftest) to account for serial correlations in the innovations process e(t). Phillips-Perron 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 p-values from the tables. Tables for tests of type 't1' and 't2' are identical to those for adftest.
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