Polynomials on vector spaces: Difference between revisions

Latest revision as of 13:25, 14 July 2013

In statistics, the Phillips–Perron test (named after Peter C. B. Phillips and Pierre Perron) is a unit root test. That is, it is used in time series analysis to test the null hypothesis that a time series is integrated of order 1. It builds on the Dickey–Fuller test of the null hypothesis $\delta =0$ in Δ $y_{t}=\delta y_{t-1}+u_{t}\,$ , where Δ is the first difference operator. Like the augmented Dickey–Fuller test, the Phillips–Perron test addresses the issue that the process generating data for $y_{t}$ might have a higher order of autocorrelation than is admitted in the test equation - making $y_{t-1}$ endogenous and thus invalidating the Dickey–Fuller t-test. Whilst the augmented Dickey–Fuller test addresses this issue by introducing lags of Δ $y_{t}$ as regressors in the test equation, the Phillips–Perron test makes a non-parametric correction to the t-test statistic. The test is robust with respect to unspecified autocorrelation and heteroscedasticity in the disturbance process of the test equation.

Davidson and MacKinnon (2004) report that the Phillips–Perron test performs worse in finite samples than the augmented Dickey-Fuller test.

References

Davidson, Russell and James G. MacKinnon (2004), Econometric Theory and Methods, p. 623, ISBN 978-0-19-512372-2
Phillips, P.C.B and P. Perron (1988), "Testing for a Unit Root in Time Series Regression", Biometrika, 75, 335–346

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+In [[statistics]], the '''Phillips–Perron test''' (named after Peter C. B. Phillips and Pierre Perron) is a [[unit root]] test.  That is, it is used in [[time series]] analysis to test the [[null hypothesis]] that a time series is [[order of integration|integrated of order]] 1.  It builds on the [[Dickey–Fuller test]] of the null hypothesis <math>\delta = 0</math> in Δ <math>y_{t}= \delta y_{t-1}+u_{t}\,</math>, where Δ is the [[first difference]] [[Operator (mathematics)|operator]]. Like the [[augmented Dickey–Fuller test]], the '''Phillips–Perron test''' addresses the issue that the process generating data for <math>y_{t}</math> might have a higher order of autocorrelation than is admitted in the test equation - making <math>y_{t-1}</math> endogenous and thus invalidating the Dickey–Fuller '''[[t-test]]'''. Whilst the [[augmented Dickey–Fuller test]] addresses this issue by introducing lags of Δ <math>y_{t}</math> as regressors in the test equation, the Phillips–Perron test makes a [[non-parametric statistics|non-parametric]] correction to the t-test statistic. The test is robust with respect to unspecified [[autocorrelation]] and [[heteroscedasticity]] in the disturbance process of the test equation.
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+Davidson and MacKinnon (2004) report that the Phillips–Perron test performs worse in finite samples than the [[augmented Dickey-Fuller test]].
+==References==
+* Davidson, Russell and James G. MacKinnon (2004), Econometric Theory and Methods, p.&nbsp;623, ISBN 978-0-19-512372-2
+* Phillips, P.C.B and P. Perron (1988), "Testing for a Unit Root in Time Series Regression", ''[[Biometrika]]'', 75, 335–346
+{{DEFAULTSORT:Phillips-Perron test}}
+[[Category:Statistical tests]]

Polynomials on vector spaces: Difference between revisions

Latest revision as of 13:25, 14 July 2013

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