UnitRootTest

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

UnitRootTest[data, model, "property"]
returns the value of for a given model.

Details and OptionsDetails and Options

  • UnitRootTest performs a hypothesis 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 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
    r
    "Constant" and
    "Drift"
    {"Constant",r}
    {"Drift", r}general case
  • UnitRootTest[data] will choose Dickey-Fuller 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 .
  • The following tests can be used:
  • "DickeyFullerF"based on
    "DickeyFullerT"based on
    "PhillipsPerronF"adjusted Dickey-Fuller F test
    "PhillipsPerronT"adjusted Dickey-Fuller 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 .
  • 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 and properties is controlled by the SignificanceLevel option. By default, is set to .

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

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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Test whether a time series has a unit root:

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The data did not come from a weakly stationary process:

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