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 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>

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==

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==References==

{{Reflist}}

* {{Cite journal | last1 = Bhargava | first1 = A. | authorlink = Alok Bhargava| title = On the Theory of Testing for Unit Roots in Observed Time Series | journal = [[The Review of Economic Studies]] | volume = 53 | issue = 3 | pages = 369–384 | doi = 10.2307/2297634 | jstor = 2297634| year = 1986 | pmid = | pmc = }}

* Bierens, H.J. (2001). "Unit Roots," Ch. 29 in ''A Companion to Econometric Theory'', editor B. Baltagi, Oxford: [[Blackwell Publishers]], 610–633. [http://econ.la.psu.edu/~hbierens/UNITROOT.PDF "2007 revision"]