BUILT-IN MATHEMATICA SYMBOL

# 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:
•  SignificanceLevel 0.05 cutoff 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:

 Out[2]=

The data came from a weakly stationary process:

 Out[3]=

Test whether a time series has a unit root:

 Out[2]=

The data did not come from a weakly stationary process:

 Out[3]=

### Neat Examples (1)Neat Examples (1)

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