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</math> can be written as,
<math>y_t =
where,
* <math>
</math> is the deterministic component (trend, seasonal component, etc.)
* <math>\varepsilon_t▼
</math> is the stationary error process. ▼
* <math>z_t
</math> is the stochastic component.
▲* <math>\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.<ref>{{Citation |title=Elements of Time Series Econometrics: An Applied Approach|last1=Kočenda|first1=Evžen |last2= Alexandr| first2= Černý |publisher= [[Karolinum Press]] |year=2014|isbn=978-80-246-2315-3|pages=66}}.</ref>
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