EstimatedProcess

EstimatedProcess[data,proc]
estimates the parametric process proc from data.

EstimatedProcess[data,proc,{{p, p0}, {q, q0},}]
estimates the parameters p, q, with starting values , , .

EstimatedProcess[data,proc,iproc]
estimates process proc with starting values taken from the instantiated process iproc.

Details and OptionsDetails and Options

  • EstimatedProcess returns the symbolic process proc with parameter estimates inserted for any non-numeric values.
  • The data can be given in the following forms:
  • {s0,}a path with state at time i
    {{t0,s0},}a path with state at time
    TemporalData[]one or several paths
  • The times and states must belong to the time and state domain of the process proc.
  • The process proc can be any parametric scalar- or vector-valued process.
  • The following options can be given:
  • AccuracyGoalAutomaticthe accuracy sought
    ProcessEstimatorAutomaticwhat process parameter estimator to use
    PrecisionGoalAutomaticthe precision sought
    WorkingPrecisionAutomaticthe precision used in internal computations
  • The following basic settings can be used for ProcessEstimator:
  • Automaticautomatically choose the parameter estimator
    "MaximumLikelihood"maximize the log likelihood directly
    Hold[Transmogrify`Private`out]"MethodOfMoments"match covariance
  • Special settings for ProcessEstimator are documented under the individual random process reference pages.
  • Additional settings for time series processes include and .
  • Additonal settings for HiddenMarkovProcess include and .

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Estimate the parameter of a PoissonProcess:

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Compare simulations of the estimated process to the original data:

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Find parameters for an ARProcess:

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Compare correlation functions for data and the estimated process:

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Introduced in 2012
(9.0)