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In statistics, the Phillips–Perron test 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 in , where is the first difference operator. Like the augmented Dickey–Fuller test, the Phillips–Perron test addresses the issue that the process generating data for might have a higher order of autocorrelation than is admitted in the test equation—making endogenous and thus invalidating the Dickey–Fuller t-test. Whilst the augmented Dickey–Fuller test addresses this issue by introducing lags of 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.
In statistics, a sequence of random variables is homoscedastic if all its random variables have the same finite variance. This is also known as homogeneity of variance. The complementary notion is called heteroscedasticity. The spellings homoskedasticity and heteroskedasticity are also frequently used.
References
- 1 2 Ljung, G. M.; Box, G. E. P. (1978). "On a measure of lack of fit in time series models" (PDF). Biometrika . 65 (2): 297–303. doi:10.1093/biomet/65.2.297. Archived from the original on September 23, 2017.
- ↑ Box, G. E. P.; Pierce, D. A. (1970). "Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models". Journal of the American Statistical Association . 65 (332): 1509–1526. doi:10.1080/01621459.1970.10481180. JSTOR 2284333.
- ↑ Castle, Jennifer L.; Hendry, David F. (2010). "A Low-Dimension Portmanteau Test for Non-linearity" (PDF). Journal of Econometrics . 158 (2): 231–245. doi:10.1016/j.jeconom.2010.01.006.
- Enders, W. (1995). Applied Econometric Time Series . New York: John Wiley & Sons. pp. 86–87. ISBN 0471039411.
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