Documentation |
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:
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 Dickey-Fuller statistics (see adftest) to account for serial correlations in the innovations process e(t).
y |
Vector of time-series data. The last element is the most recent observation. NaNs indicating missing values are removed. |
'lags' |
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. Default: 0 |
'model' |
String or cell vector of strings indicating the model variant. Values are:
Default: 'AR' |
'test' |
String or cell vector of strings indicating the test statistic. Values are:
Default: 't1' |
'alpha' |
Scalar or vector of nominal significance levels for the tests. Set values between 0.001 and 0.999. Default: 0.05 |
The Phillips-Perron model is
y_{t} = c + δt + a y_{t – 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).
[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.
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