tests whether the data is autocorrelated.


tests whether the data is autocorrelated up to lag k.


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

Details and Options

  • AutocorrelationTest performs a hypothesis test for randomness on data with the null hypothesis that the autocorrelations ρ1=ρ2==ρk==0 and alternative that at least one of the ρi0.
  • Rejecting the null hypothesis allows the conclusion that the data is not random.
  • By default, a probability value or -value is returned.
  • A small -value suggests that randomness is unlikely.
  • The data can be a list of values {x1,x2,,xn} or a TemporalData object.
  • The lag k can be Automatic or a positive integer such that k<n.
  • If k is not given, it is taken to be Automatic.
  • Setting k to Automatic gives k=Ceiling[Log[n]]].
  • AutocorrelationTest[data,k,"test"] reports the -value according to "test".
  • The following tests can be used for univariate data with all paths of equal length n:
  • "LjungBox"
  • For multivariate data:
  • "LjungBox"
    "BoxPierce"n sum_(i=1)^kTr[TemplateBox[{{(, {gamma, _, i}, )}}, Transpose].TemplateBox[{{(, {gamma, _, 0}, )}}, Inverse].gamma_i.TemplateBox[{{(, {gamma, _, 0}, )}}, Inverse]]
  • AutocorrelationTest[data,k,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • AutocorrelationTest[data,k,"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.


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Basic Examples  (1)

Test whether data is random:

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The data is autocorrelated:

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Scope  (14)

Options  (1)

Applications  (2)

Possible Issues  (1)

See Also

HypothesisTestData  TimeSeriesModelFit  ARProcess  MAProcess  ARMAProcess  ARIMAProcess  FARIMAProcess  SARMAProcess  SARIMAProcess  RandomFunction  LocationTest  IndependenceTest

Introduced in 2014