Unit root test: Difference between revisions

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In [[statistics]], a '''unit root test''' tests whether a [[time series]] variable is non-stationary using an [[autoregressive]] model.

In [[statistics]], a '''unit root test''' tests whether a [[time series]] variable is non-stationary using an [[autoregressive]] model. A commonly used test that is valid in large samples is the [[augmented Dickey–Fuller test]]. The optimal finite sample tests for a unit root in autoregressive models were developed by [[Denis Sargan]] and [[Alok Bhargava]] by extending the work by [[John von Neumann]], and [[James Durbin]] and [[Geoffrey Watson]]. In the observed time series cases, for example, Sargan-Bhargava statistics test the unit root null hypothesis in first order autoregressive models against one-sided alternatives, i.e., if the process is stationary or explosive under the alternative hypothesis. Another test is the [[Phillips–Perron test]].

In general, the approach to unit root testing implicitly assumes that the time series to be tested <math>[y_t]_{t=1}^T

</math> can be written as,

<math>y_t = TD_t + z_t + \varepsilon_t </math>

where,

* <math>TD_t

</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.

The task of the test is to determine whether the stochastic component contains a unit root or is stationary.<ref>{{Cite book|title=Elements of Time Series Econometrics: As Applied Approach|last=Kocenda|first=Evzen|publisher=Charles University in Prague|year=2014|isbn=978-80-246-2315-3|___location=Pargue|pages=66}}</ref>

In [[statistics]], a '''unit root test''' tests whether a [[time series]] variable is non-stationary using an [[autoregressive]] model. A commonly used test that is valid in large samples is the [[augmented Dickey–Fuller test]]. The optimal finite sample tests for a unit root in autoregressive models were developed by [[Denis Sargan]] and [[Alok Bhargava]] by extending the work by [[John von Neumann]], and [[James Durbin]] and [[Geoffrey Watson]]. In the observed time series cases, for example, Sargan-Bhargava statistics test the unit root null hypothesis in first order autoregressive models against one-sided alternatives, i.e., if the process is stationary or explosive under the alternative hypothesis. Another test is the [[Phillips–Perron test]].

==See also==