Unit root test: Difference between revisions

Revision as of 09:40, 20 October 2019

Revision as of 22:48, 11 December 2019

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== Main tests ==

A commonly used test that is valid in large samples is the [[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> The optimal finite sample tests for a unit root in autoregressive models were developed by [[Denis Sargan]] and [[Alok Bhargava]],<ref>{{Cite journal | last1 = Sargan | first1 = J. D. | last2 = Bhargava | first2 = Alok | year = 1983 | title = Testing residuals from least squares regression for being generated by the Gaussian random walk | journal = [[Econometrica]] | volume = 51 | issue = 1 | pages = 153–174 | publisher = | jstor = 1912252 | doi= | url = | format = | accessdate = }}</ref> 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.

Other popular tests include:

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==References==

* {{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 = }}

*{{cite book |last=Bierens, |first=H. J. (|year=2001). "|chapter=Unit roots", Ch. 29 in ''|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"]

* {{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}}

*{{cite book |last=Enders |first=Walter |title=Applied Econometric Time Series |publisher=[[John Wiley & Sons]] |year=2004 |edition=Second |pages=170–175 |isbn=0-471-23065-0 |url-access=registration |url=https://archive.org/details/appliedeconometr00ende_0 }}

*{{citation | first= K. | last= Patterson | title= Unit Root Tests in Time Series | volume= 1 | year= 2011 | publisher= [[Palgrave Macmillan]]}}.

*{{citation | first= K. | last= Patterson | title= Unit Root Tests in Time Series | volume= 2 | year= 2012 | publisher= [[Palgrave Macmillan]]}}.

* {{Cite journal | last1 = Sargan | first1 = J. D. | last2 = Bhargava | first2 = Alok | year = 1983 | title = Testing residuals from least squares regression for being generated by the Gaussian random walk | journal = [[Econometrica]] | volume = 51 | issue = 1 | pages = 153–174 | publisher = | jstor = 1912252 | doi= | url = | format = | accessdate = }}

[[Category:Time series statistical tests]]