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.



References

2016

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.