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 option 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.


open all close all

Basic Examples  (1)

Test whether a time series has a unit root:

Click for copyable input
Click for copyable input

The data came from a weakly stationary process:

Click for copyable input

Scope  (17)

Options  (1)

Applications  (3)

Possible Issues  (2)

Neat Examples  (2)

Introduced in 2012