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FindProcessParameters[data,proc]

finds the parameter estimates for the process proc from data.

FindProcessParameters[data,proc,{{p,p0},{q,q0},…}]

finds the parameters p, q, … with starting values p0, q0, … .

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Parametric Processes  
Time Series Processes  
Queueing Processes  
Finite Markov Processes  
Options  
WorkingPrecision  
ProcessEstimator  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

FindProcessParameters

FindProcessParameters[data,proc]

finds the parameter estimates for the process proc from data.

FindProcessParameters[data,proc,{{p,p0},{q,q0},…}]

finds the parameters p, q, … with starting values p0, q0, … .

Details and Options

  • FindProcessParameters returns a list of replacement rules for the parameters in proc.
  • The data can be given in the following forms:
  • {s0,…}a path with state si at time i
    {{t0,s0},…}a path with state si at time ti
    TemporalData[…]one or several paths
  • The times ti and states si 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
    ProcessEstimator Automaticwhat process parameter estimator to use
    PrecisionGoalAutomaticthe precision sought
    WorkingPrecision Automaticthe 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
    "MethodOfMoments"match covariance
  • Special settings for ProcessEstimator are documented under the individual random process reference pages.
  • Additional settings for time series processes include "MaximumConditionalLikelihood" and "SpectralEstimator".
  • Additional settings for HiddenMarkovProcess include "BaumWelch" and "ViterbiTraining".

Examples

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Basic Examples  (2)

Estimate the parameter of a PoissonProcess:

Obtain the estimated process:

Compare simulations of the estimated process to the original data:

Find the parameters for an ARProcess:

Obtain the estimated process:

Compare correlation functions for data and the estimated process:

Scope  (9)

Parametric Processes  (3)

Estimate the parameter for a RandomWalkProcess:

Estimate the parameters for a RenewalProcess:

Estimate the parameters for a Wiener process:

Time Series Processes  (3)

Estimate the parameters for an ARProcess:

Compare covariance functions:

Estimate an ARMAProcess:

Compare covariance functions:

Provide initial values for the estimation of an ARProcess:

Solve for repeated parameters:

Queueing Processes  (2)

Estimate the arrival and service rates for an M/M/1 queue:

Use the corresponding random path for the data:

Estimate the arrival rate for an M/M/1 queue:

Estimate the service rate:

Finite Markov Processes  (1)

Estimate the parameters for a discrete Markov process:

Options  (5)

WorkingPrecision  (1)

Estimate process parameters using default machine precision:

Use higher precision:

ProcessEstimator  (4)

Maximum likelihood for a parametric process:

Time series process:

Method of moments for a parametric process:

Time series process:

Maximize conditional likelihood for a time series process:

Spectral estimator for a time series process:

Applications  (2)

Model the mean daily temperature for Champaign in August 2012:

Find process parameters:

Compare CorrelationFunction of the model and the data:

The daily exchange rates of the euro to the dollar from May 2012 through September 2012:

Fit an AR process to the exchange rates:

Forecast for 20 business days ahead:

Plot the forecast with original data:

Properties & Relations  (2)

FindProcessParameters returns a list of parameter estimates for a process:

EstimatedProcess estimates the parametric process:

FindProcessParameters returns a list of parameter estimates for a process:

FindDistributionParameters returns a list of parameter estimates for a distribution:

Wolfram Research (2012), FindProcessParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindProcessParameters.html.

Text

Wolfram Research (2012), FindProcessParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindProcessParameters.html.

CMS

Wolfram Language. 2012. "FindProcessParameters." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindProcessParameters.html.

APA

Wolfram Language. (2012). FindProcessParameters. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindProcessParameters.html

BibTeX

@misc{reference.wolfram_2025_findprocessparameters, author="Wolfram Research", title="{FindProcessParameters}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/FindProcessParameters.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_findprocessparameters, organization={Wolfram Research}, title={FindProcessParameters}, year={2012}, url={https://reference.wolfram.com/language/ref/FindProcessParameters.html}, note=[Accessed: 01-December-2025]}