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.

== General approach ==

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,

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* <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>{{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>

== Main tests ==

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]].

Other popular tests include:

==See also==

* [[Augmented Dickey–Fuller test]]

* [[Dickey–Fuller test]]

* [[Phillips–Perron test]]

* [[KPSS test]] (in which the null hypothesis is [[Trend stationary|trend stationarity]] rather than [[Stationary process|stationarity]])

* [[KPSS test]]

* [[Zivot–Andrews test]]

* [[ADF-GLS test]]

* [[Dickey–FullerZivot–Andrews test]]

Unit root tests are closely linked to [[Autocorrelation|serial correlation]] tests. However, while all processes with a unit root will exhibit serial correlation, not all serially correlated time series will have a unit root. Popular serial correlation tests include:

* [[Breusch–Godfrey test]]

* [[KPSSLjung–Box test]]

* [[Durbin–Watson statistic|Durbin–Watson test]]

==Notes==

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[[Category:Statistical tests]]

[[Category:Time series analysis]]

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