Unit Root Test
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A Unit Root Test is a statistical test of whether a time series variable is a stationary process and has a unit root.
- See: Time Series Analysis, Dickey–Fuller Test, Phillips–Perron Test, KPSS Test, Breusch–Godfrey Test, Ljung–Box Test, Durbin–Watson Test, Augmented Dickey–Fuller Test.
References
2016
- (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Unit_root_test Retrieved 2016-08-07
- In statistics, a unit root test tests whether a time series variable is non-stationary and possesses a unit root. The null hypothesis is generally defined as the presence of a unit root and the alternative hypothesis is either stationarity, trend stationarity or explosive root depending on the test used.
- General approach
- In general, the approach to unit root testing implicitly assumes that the time series to be tested [math]\displaystyle{ [y_t]_{t=1}^T }[/math] can be written as,
- [math]\displaystyle{ y_t = D_t + z_t + \varepsilon_t }[/math]
- where,
- [math]\displaystyle{ D_t }[/math] is the deterministic component (trend, seasonal component, etc.)
- [math]\displaystyle{ z_t }[/math] is the stochastic component.
- [math]\displaystyle{ \varepsilon_t }[/math] is the stationary error process.
- The task of the test is to determine whether the stochastic component contains a unit root or is stationary.
- where,