{{Short description|Time series statistical test}} In statistics, a '''unit root test''' tests whether a time series variable is non-stationary and possesses a unit root. The null hypothesis is generally defined as the presence of a unit root and the alternative hypothesis is either stationarity, trend stationarity or explosive root depending on the test used.
== 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,
:<math>y_t = D_t + z_t + \varepsilon_t </math>
where, * <math>D_t
</math> is the deterministic component (trend, seasonal component, etc.) * <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>
== Main tests ==
Other popular tests include: * augmented Dickey–Fuller test<ref>{{Cite journal | doi = 10.1080/01621459.1979.10482531| title = Distribution of the estimators for autoregressive time series with a unit root| year = 1979| last1 = Dickey | first1 = D. A. | last2 = Fuller | first2 = W. A. | journal = Journal of the American Statistical Association | volume = 74| issue = 366a| pages = 427–431}}</ref> *: this is valid in large samples. * Phillips–Perron test * KPSS test *: here the null hypothesis is trend stationarity rather than the presence of a unit root. * ADF-GLS test Unit root tests are closely linked to 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 * Ljung–Box test * Durbin–Watson test
==Notes== {{Notelist}}
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==References== *{{cite book |last=Bierens |first=H. J. |year=2001 |chapter=Unit roots |title=A Companion to Econometric Theory |editor-first=B. |editor-last=Baltagi |location=Oxford |publisher=Blackwell Publishers |pages=610–633 }} [http://econ.la.psu.edu/~hbierens/UNITROOT.PDF "2007 revision"] {{Webarchive|url=https://web.archive.org/web/20140617113943/http://econ.la.psu.edu/~hbierens/UNITROOT.PDF |date=2014-06-17 }} *{{cite book |last=Enders |first=Walter |title=Applied Econometric Time Series |publisher=John Wiley & Sons |year=2004 |edition=Second |pages=[https://archive.org/details/appliedeconometr00ende_0/page/170 170–175] |isbn=0-471-23065-0 |url-access=registration |url=https://archive.org/details/appliedeconometr00ende_0/page/170 }} *{{cite book |last=Maddala |first=G. S. |authorlink=G. S. Maddala |last2=Kim |first2=In-Moo |chapter=Issues in Unit Root Testing |title=Unit Roots, Cointegration, and Structural Change |url=https://archive.org/details/unitrootscointeg00madd |url-access=limited |location=Cambridge |publisher=Cambridge University Press |year=1998 |isbn=0-521-58782-4 |pages=[https://archive.org/details/unitrootscointeg00madd/page/n116 98]–154 }}
Category:Time series statistical tests