tests whether data came from an autoregressive time series process with unit root.


returns the value of "property" for a given model.

Details and Options

  • UnitRootTest performs a hypothesis test on the time series data with the null hypothesis that the time series satisfying an AR model has a unit root in the denominator of the corresponding transfer function and the alternative hypothesis that it does not.
  • Rejecting the null hypothesis allows the conclusion that the detrended data could have come from a stationary time series.
  • By default, a probability value or -value is returned.
  • A small -value suggests that the presence of a unit root is unlikely.
  • The data can be a list of values {x1,x2,,xn} or a TemporalData object.
  • The model allows the specification of a model , where is the constant offset, is a linear drift, and is the order of the AR model.
  • The following model specifications can be used:
  • Automatic and
    "Constant" and
    {"Drift", r}general case
  • UnitRootTest[data] will choose DickeyFuller F test with and .
  • UnitRootTest[data,model,All] will choose all tests that apply to data and model.
  • UnitRootTest[data,model,"test"] reports the -value according to "test".
  • The following tests can be used:
  • "DickeyFullerF"based on
    "DickeyFullerT"based on
    "PhillipsPerronF"adjusted DickeyFuller F test
    "PhillipsPerronT"adjusted DickeyFuller T test
  • UnitRootTest[data,model,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • UnitRootTest[data,model,"property"] can be used to directly give the value of "property".
  • Properties related to the reporting of test results include:
  • "AllTests"list of all applicable tests
    "AutomaticTest"test chosen if Automatic is used
    "PValue"list of -values
    "PValueTable"formatted table of -values
    "ShortTestConclusion"a short description of the conclusion of a test
    "TestConclusion"a description of the conclusion of a test
    "TestData"list of pairs of test statistics and -values
    "TestDataTable"formatted table of -values and test statistics
    "TestStatistic"list of test statistics
    "TestStatisticTable"formatted table of test statistics
  • The following options can be used:
  • SignificanceLevel0.05cutoff for diagnostics and reporting
  • For unit root tests, a cutoff is chosen such that is rejected only if . The value of used for the "TestConclusion" and "ShortTestConclusion" properties is controlled by the SignificanceLevel option. By default, is set to 0.05.


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Basic Examples  (1)

Test whether a time series has a unit root:

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The data came from a weakly stationary process:

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Scope  (17)

Options  (1)

Applications  (3)

Possible Issues  (2)

Neat Examples  (2)

See Also

HypothesisTestData  ARProcess  MAProcess  ARMAProcess  ARIMAProcess  FARIMAProcess  SARMAProcess  SARIMAProcess  RandomFunction  LocationTest  IndependenceTest

Introduced in 2012