Unit Root Test

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.

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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.

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