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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 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 
.
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